Hands-on Exercise 10:Spatial Interaction Models

Author

Sei Sar Hla Kyi

Published

October 31, 2024

Modified

October 31, 2024

15  Processing and Visualising Flow Data

Spatial interaction represent the flow of people, material, or information between locations in geographical space. It encompasses everything from freight shipments, energy flows, and the global trade in rare antiquities, to flight schedules, rush hour woes, and pedestrian foot traffic.

Each spatial interaction, as an analogy for a set of movements, is composed of a discrete origin/destination pair. Each pair can be represented as a cell in a matrix where rows are related to the locations (centroids) of origin, while columns are related to locations (centroids) of destination. Such a matrix is commonly known as an origin/destination matrix, or a spatial interaction matrix.

In this hands-on exercise, you will learn how to build an OD matrix by using Passenger Volume by Origin Destination Bus Stops data set downloaded from LTA DataMall. By the end of this hands-on exercise, you will be able:

  • to import and extract OD data for a selected time interval,

  • to import and save geospatial data (i.e. bus stops and mpsz) into sf tibble data frame objects,

  • to populate planning subzone code into bus stops sf tibble data frame,

  • to construct desire lines geospatial data from the OD data, and

  • to visualise passenger volume by origin and destination bus stops by using the desire lines data.

Load packages

pacman::p_load(tmap, sf, DT, stplanr, tidyverse, sp,
               performance, reshape2,
               ggpubr)

Preparing the Flow Data

Importing the OD data

odbus <- read_csv("data/aspatial/origin_destination_bus_202210.csv")
glimpse(odbus)
Rows: 5,122,925
Columns: 7
$ YEAR_MONTH          <chr> "2022-10", "2022-10", "2022-10", "2022-10", "2022-…
$ DAY_TYPE            <chr> "WEEKDAY", "WEEKENDS/HOLIDAY", "WEEKENDS/HOLIDAY",…
$ TIME_PER_HOUR       <dbl> 10, 10, 7, 11, 16, 16, 20, 7, 7, 11, 11, 8, 11, 11…
$ PT_TYPE             <chr> "BUS", "BUS", "BUS", "BUS", "BUS", "BUS", "BUS", "…
$ ORIGIN_PT_CODE      <dbl> 65239, 65239, 23519, 52509, 54349, 54349, 43371, 8…
$ DESTINATION_PT_CODE <dbl> 65159, 65159, 23311, 42041, 53241, 53241, 14139, 9…
$ TOTAL_TRIPS         <dbl> 2, 1, 2, 1, 1, 4, 1, 3, 1, 5, 2, 5, 15, 40, 1, 1, …

A quick check of odbus tibble data frame shows that the values in OROGIN_PT_CODE and DESTINATON_PT_CODE are in numeric data type. Hence, the code chunk below is used to convert these data values into character data type.

odbus$ORIGIN_PT_CODE <- as.factor(odbus$ORIGIN_PT_CODE)
odbus$DESTINATION_PT_CODE <- as.factor(odbus$DESTINATION_PT_CODE) 

Extracting the study data

We will extract commuting flows on weekday and between 6 and 9 o’clock.

odbus6_9 <- odbus %>%
  filter(DAY_TYPE == "WEEKDAY") %>%
  filter(TIME_PER_HOUR >= 6 &
           TIME_PER_HOUR <= 9) %>%
  group_by(ORIGIN_PT_CODE,
           DESTINATION_PT_CODE) %>%
  summarise(TRIPS = sum(TOTAL_TRIPS))
datatable(odbus6_9)
write_rds(odbus6_9, "data/rds/odbus6_9.rds")
odbus6_9 <- read_rds("data/rds/odbus6_9.rds")

Working with Geospatial Data

busstop <- st_read(dsn = "data/geospatial",
                   layer = "BusStop") %>%
  st_transform(crs = 3414)
Reading layer `BusStop' from data source 
  `/Users/seesarhlakyi/Desktop/ssrhk/ISSS626-GAA/Hands-on_Ex/Hands-on_Ex10/data/geospatial' 
  using driver `ESRI Shapefile'
Simple feature collection with 5159 features and 3 fields
Geometry type: POINT
Dimension:     XY
Bounding box:  xmin: 3970.122 ymin: 26482.1 xmax: 48284.56 ymax: 52983.82
Projected CRS: SVY21
mpsz <- st_read(dsn = "data/geospatial",
                   layer = "MPSZ-2019") %>%
  st_transform(crs = 3414)
Reading layer `MPSZ-2019' from data source 
  `/Users/seesarhlakyi/Desktop/ssrhk/ISSS626-GAA/Hands-on_Ex/Hands-on_Ex10/data/geospatial' 
  using driver `ESRI Shapefile'
Simple feature collection with 332 features and 6 fields
Geometry type: MULTIPOLYGON
Dimension:     XY
Bounding box:  xmin: 103.6057 ymin: 1.158699 xmax: 104.0885 ymax: 1.470775
Geodetic CRS:  WGS 84
mpsz
Simple feature collection with 332 features and 6 fields
Geometry type: MULTIPOLYGON
Dimension:     XY
Bounding box:  xmin: 2667.538 ymin: 15748.72 xmax: 56396.44 ymax: 50256.33
Projected CRS: SVY21 / Singapore TM
First 10 features:
                 SUBZONE_N SUBZONE_C       PLN_AREA_N PLN_AREA_C       REGION_N
1              MARINA EAST    MESZ01      MARINA EAST         ME CENTRAL REGION
2         INSTITUTION HILL    RVSZ05     RIVER VALLEY         RV CENTRAL REGION
3           ROBERTSON QUAY    SRSZ01  SINGAPORE RIVER         SR CENTRAL REGION
4  JURONG ISLAND AND BUKOM    WISZ01  WESTERN ISLANDS         WI    WEST REGION
5             FORT CANNING    MUSZ02           MUSEUM         MU CENTRAL REGION
6         MARINA EAST (MP)    MPSZ05    MARINE PARADE         MP CENTRAL REGION
7                   SUDONG    WISZ03  WESTERN ISLANDS         WI    WEST REGION
8                  SEMAKAU    WISZ02  WESTERN ISLANDS         WI    WEST REGION
9           SOUTHERN GROUP    SISZ02 SOUTHERN ISLANDS         SI CENTRAL REGION
10                 SENTOSA    SISZ01 SOUTHERN ISLANDS         SI CENTRAL REGION
   REGION_C                       geometry
1        CR MULTIPOLYGON (((33222.98 29...
2        CR MULTIPOLYGON (((28481.45 30...
3        CR MULTIPOLYGON (((28087.34 30...
4        WR MULTIPOLYGON (((14557.7 304...
5        CR MULTIPOLYGON (((29542.53 31...
6        CR MULTIPOLYGON (((35279.55 30...
7        WR MULTIPOLYGON (((15772.59 21...
8        WR MULTIPOLYGON (((19843.41 21...
9        CR MULTIPOLYGON (((30870.53 22...
10       CR MULTIPOLYGON (((26879.04 26...
st_read() function of sf package is used to import the shapefile into R as sf data frame. st_transform() function of sf package is used to transform the projection to crs 3414.
mpsz <- write_rds(mpsz, "data/rds/mpsz.rds")

Geospatial data wrangling

busstop_mpsz <- st_intersection(busstop, mpsz) %>%
  select(BUS_STOP_N, SUBZONE_C) %>%
  st_drop_geometry()
datatable(busstop_mpsz)
od_data <- left_join(odbus6_9 , busstop_mpsz,
            by = c("ORIGIN_PT_CODE" = "BUS_STOP_N")) %>%
  rename(ORIGIN_BS = ORIGIN_PT_CODE,
         ORIGIN_SZ = SUBZONE_C,
         DESTIN_BS = DESTINATION_PT_CODE)

If duplicated records are found, the code chunk below will be used to retain the unique records.

duplicate <- od_data %>%
  group_by_all() %>%
  filter(n()>1) %>%
  ungroup()
od_data <- unique(od_data)
od_data <- left_join(od_data , busstop_mpsz,
            by = c("DESTIN_BS" = "BUS_STOP_N")) 
duplicate <- od_data %>%
  group_by_all() %>%
  filter(n()>1) %>%
  ungroup()
od_data <- unique(od_data)
od_data <- od_data %>%
  rename(DESTIN_SZ = SUBZONE_C) %>%
  drop_na() %>%
  group_by(ORIGIN_SZ, DESTIN_SZ) %>%
  summarise(MORNING_PEAK = sum(TRIPS))
write_rds(od_data, "data/rds/od_data_fii.rds")
od_data_fii <- read_rds("data/rds/od_data.rds")

Visualising Spatial Interaction

Removing intra-zonal flows

od_data_fij <- od_data[od_data$ORIGIN_SZ!=od_data$DESTIN_SZ,]
write_rds(od_data_fij, "data/rds/od_data_fij.rds")
od_data_fij <- read_rds("data/rds/od_data_fij.rds")

Creating desire lines

flowLine <- od2line(flow = od_data_fij, 
                    zones = mpsz,
                    zone_code = "SUBZONE_C")
write_rds(flowLine, "data/rds/flowLine.rds")
flowLine <- read_rds("data/rds/flowLine.rds")

Visualising the desire lines

tm_shape(mpsz) +
  tm_polygons() +
flowLine %>%  
tm_shape() +
  tm_lines(lwd = "MORNING_PEAK",
           style = "quantile",
           scale = c(0.1, 1, 3, 5, 7, 10),
           n = 6,
           alpha = 0.3)

When the flow data are very messy and highly skewed like the one shown above, it is wiser to focus on selected flows, for example flow greater than or equal to 5000 as shown below.

tm_shape(mpsz) +
  tm_polygons() +
flowLine %>%  
  filter(MORNING_PEAK >= 5000) %>%
tm_shape() +
  tm_lines(lwd = "MORNING_PEAK",
           style = "quantile",
           scale = c(0.1, 1, 3, 5, 7, 10),
           n = 6,
           alpha = 0.3)

16  Calibrating Spatial Interaction Models with R

Spatial Interaction Models (SIMs) are mathematical models for estimating flows between spatial entities developed by Alan Wilson in the late 1960s and early 1970, with considerable uptake and refinement for transport modelling since then Boyce and Williams (2015).

There are four main types of traditional SIMs (Wilson 1971):

  • Unconstrained

  • Production-constrained

  • Attraction-constrained

  • Doubly-constrained

Ordinary least square (OLS), log-normal, Poisson and negative binomial (NB) regression methods have been used extensively to calibrate OD flow models by processing flow data as different types of dependent variables. In this chapter, you will gain hands-on experiences on using appropriate R packages to calibrate SIM by using there four regression methods.

Computing Distance Matrix

mpsz <- read_rds("data/rds/mpsz.rds")
mpsz
Simple feature collection with 332 features and 6 fields
Geometry type: MULTIPOLYGON
Dimension:     XY
Bounding box:  xmin: 2667.538 ymin: 15748.72 xmax: 56396.44 ymax: 50256.33
Projected CRS: SVY21 / Singapore TM
First 10 features:
                 SUBZONE_N SUBZONE_C       PLN_AREA_N PLN_AREA_C       REGION_N
1              MARINA EAST    MESZ01      MARINA EAST         ME CENTRAL REGION
2         INSTITUTION HILL    RVSZ05     RIVER VALLEY         RV CENTRAL REGION
3           ROBERTSON QUAY    SRSZ01  SINGAPORE RIVER         SR CENTRAL REGION
4  JURONG ISLAND AND BUKOM    WISZ01  WESTERN ISLANDS         WI    WEST REGION
5             FORT CANNING    MUSZ02           MUSEUM         MU CENTRAL REGION
6         MARINA EAST (MP)    MPSZ05    MARINE PARADE         MP CENTRAL REGION
7                   SUDONG    WISZ03  WESTERN ISLANDS         WI    WEST REGION
8                  SEMAKAU    WISZ02  WESTERN ISLANDS         WI    WEST REGION
9           SOUTHERN GROUP    SISZ02 SOUTHERN ISLANDS         SI CENTRAL REGION
10                 SENTOSA    SISZ01 SOUTHERN ISLANDS         SI CENTRAL REGION
   REGION_C                       geometry
1        CR MULTIPOLYGON (((33222.98 29...
2        CR MULTIPOLYGON (((28481.45 30...
3        CR MULTIPOLYGON (((28087.34 30...
4        WR MULTIPOLYGON (((14557.7 304...
5        CR MULTIPOLYGON (((29542.53 31...
6        CR MULTIPOLYGON (((35279.55 30...
7        WR MULTIPOLYGON (((15772.59 21...
8        WR MULTIPOLYGON (((19843.41 21...
9        CR MULTIPOLYGON (((30870.53 22...
10       CR MULTIPOLYGON (((26879.04 26...

Converting from sf data.table to SpatialPolygonsDataFrame

mpsz_sp <- as(mpsz, "Spatial")
mpsz_sp
class       : SpatialPolygonsDataFrame 
features    : 332 
extent      : 2667.538, 56396.44, 15748.72, 50256.33  (xmin, xmax, ymin, ymax)
crs         : +proj=tmerc +lat_0=1.36666666666667 +lon_0=103.833333333333 +k=1 +x_0=28001.642 +y_0=38744.572 +ellps=WGS84 +towgs84=0,0,0,0,0,0,0 +units=m +no_defs 
variables   : 6
names       : SUBZONE_N, SUBZONE_C, PLN_AREA_N, PLN_AREA_C,       REGION_N, REGION_C 
min values  : ADMIRALTY,    AMSZ01, ANG MO KIO,         AM, CENTRAL REGION,       CR 
max values  :    YUNNAN,    YSSZ09,     YISHUN,         YS,    WEST REGION,       WR 

Computing the distance matrix

SIMs often involve a large number of pairwise calculations between spatial units, so centroid distances are computationally efficient.

dist <- spDists(mpsz_sp, 
                longlat = FALSE)
head(dist, n=c(10, 10))
           [,1]       [,2]      [,3]      [,4]       [,5]      [,6]      [,7]
 [1,]     0.000  3926.0025  3939.108 20252.964  2989.9839  1431.330 19211.836
 [2,]  3926.003     0.0000   305.737 16513.865   951.8314  5254.066 16242.523
 [3,]  3939.108   305.7370     0.000 16412.062  1045.9088  5299.849 16026.146
 [4,] 20252.964 16513.8648 16412.062     0.000 17450.3044 21665.795  7229.017
 [5,]  2989.984   951.8314  1045.909 17450.304     0.0000  4303.232 17020.916
 [6,]  1431.330  5254.0664  5299.849 21665.795  4303.2323     0.000 20617.082
 [7,] 19211.836 16242.5230 16026.146  7229.017 17020.9161 20617.082     0.000
 [8,] 14960.942 12749.4101 12477.871 11284.279 13336.0421 16281.453  5606.082
 [9,]  7515.256  7934.8082  7649.776 18427.503  7801.6163  8403.896 14810.930
[10,]  6391.342  4975.0021  4669.295 15469.566  5226.8731  7707.091 13111.391
           [,8]      [,9]     [,10]
 [1,] 14960.942  7515.256  6391.342
 [2,] 12749.410  7934.808  4975.002
 [3,] 12477.871  7649.776  4669.295
 [4,] 11284.279 18427.503 15469.566
 [5,] 13336.042  7801.616  5226.873
 [6,] 16281.453  8403.896  7707.091
 [7,]  5606.082 14810.930 13111.391
 [8,]     0.000  9472.024  8575.490
 [9,]  9472.024     0.000  3780.800
[10,]  8575.490  3780.800     0.000

Labelling column and row heanders of a distance matrix

sz_names <- mpsz$SUBZONE_C
colnames(dist) <- paste0(sz_names)
rownames(dist) <- paste0(sz_names)

Pivoting distance value by SUBZONE_C

Next, we will pivot the distance matrix into a long table by using the row and column subzone codes as show in the code chunk below.

distPair <- melt(dist) %>%
  rename(dist = value)
head(distPair, 10)
     Var1   Var2      dist
1  MESZ01 MESZ01     0.000
2  RVSZ05 MESZ01  3926.003
3  SRSZ01 MESZ01  3939.108
4  WISZ01 MESZ01 20252.964
5  MUSZ02 MESZ01  2989.984
6  MPSZ05 MESZ01  1431.330
7  WISZ03 MESZ01 19211.836
8  WISZ02 MESZ01 14960.942
9  SISZ02 MESZ01  7515.256
10 SISZ01 MESZ01  6391.342

Updating intra-zonal distances

distPair %>%
  filter(dist > 0) %>%
  summary()
      Var1             Var2             dist        
 MESZ01 :   331   MESZ01 :   331   Min.   :  173.8  
 RVSZ05 :   331   RVSZ05 :   331   1st Qu.: 7149.5  
 SRSZ01 :   331   SRSZ01 :   331   Median :11890.0  
 WISZ01 :   331   WISZ01 :   331   Mean   :12229.4  
 MUSZ02 :   331   MUSZ02 :   331   3rd Qu.:16401.7  
 MPSZ05 :   331   MPSZ05 :   331   Max.   :49894.4  
 (Other):107906   (Other):107906                    
distPair$dist <- ifelse(distPair$dist == 0,
                        50, distPair$dist)
distPair %>%
  summary()
      Var1             Var2             dist      
 MESZ01 :   332   MESZ01 :   332   Min.   :   50  
 RVSZ05 :   332   RVSZ05 :   332   1st Qu.: 7097  
 SRSZ01 :   332   SRSZ01 :   332   Median :11864  
 WISZ01 :   332   WISZ01 :   332   Mean   :12193  
 MUSZ02 :   332   MUSZ02 :   332   3rd Qu.:16388  
 MPSZ05 :   332   MPSZ05 :   332   Max.   :49894  
 (Other):108232   (Other):108232                  
distPair <- distPair %>%
  rename(orig = Var1,
         dest = Var2)
write_rds(distPair, "data/rds/distPair.rds") 
distPair <- read_rds("data/rds/distPair.rds")

Preparing flow data

od_data_fii <- read_rds("data/rds/od_data_fii.rds")
flow_data <- od_data_fii %>%
  group_by(ORIGIN_SZ, DESTIN_SZ) %>% 
  dplyr::summarize(TRIPS = sum(MORNING_PEAK)) 
head(flow_data, 10)
# A tibble: 10 × 3
# Groups:   ORIGIN_SZ [1]
   ORIGIN_SZ DESTIN_SZ TRIPS
   <chr>     <chr>     <dbl>
 1 AMSZ01    AMSZ01     1998
 2 AMSZ01    AMSZ02     8289
 3 AMSZ01    AMSZ03     8971
 4 AMSZ01    AMSZ04     2252
 5 AMSZ01    AMSZ05     6136
 6 AMSZ01    AMSZ06     2148
 7 AMSZ01    AMSZ07     1620
 8 AMSZ01    AMSZ08     1925
 9 AMSZ01    AMSZ09     1773
10 AMSZ01    AMSZ10       63

Separating intra-flow from passenger volume df

flow_data$FlowNoIntra <- ifelse(
  flow_data$ORIGIN_SZ == flow_data$DESTIN_SZ, 
  0, flow_data$TRIPS)
flow_data$offset <- ifelse(
  flow_data$ORIGIN_SZ == flow_data$DESTIN_SZ, 
  0.000001, 1)

Combining passenger volume data with distance value

flow_data$ORIGIN_SZ <- as.factor(flow_data$ORIGIN_SZ)
flow_data$DESTIN_SZ <- as.factor(flow_data$DESTIN_SZ)
flow_data1 <- flow_data %>%
  left_join (distPair,
             by = c("ORIGIN_SZ" = "orig",
                    "DESTIN_SZ" = "dest"))

Preparing Origin and Destination Attributes

Importing population data

pop <- read_csv("data/aspatial/pop.csv")

Geospatial data wrangling

pop <- pop %>%
  left_join(mpsz,
            by = c("PA" = "PLN_AREA_N",
                   "SZ" = "SUBZONE_N")) %>%
  select(1:6) %>%
  rename(SZ_NAME = SZ,
         SZ = SUBZONE_C)

Preparing origin attribute

flow_data1 <- flow_data1 %>%
  left_join(pop,
            by = c(ORIGIN_SZ = "SZ")) %>%
  rename(ORIGIN_AGE7_12 = AGE7_12,
         ORIGIN_AGE13_24 = AGE13_24,
         ORIGIN_AGE25_64 = AGE25_64) %>%
  select(-c(PA, SZ_NAME))

Preparing destination attribute

flow_data1 <- flow_data1 %>%
  left_join(pop,
            by = c(DESTIN_SZ = "SZ")) %>%
  rename(DESTIN_AGE7_12 = AGE7_12,
         DESTIN_AGE13_24 = AGE13_24,
         DESTIN_AGE25_64 = AGE25_64) %>%
  select(-c(PA, SZ_NAME))
write_rds(flow_data1, "data/rds/flow_data_6-9.rds")

Calibrating Spatial Interaction Models

Importing the modelling data

SIM_data <- read_rds("data/rds/flow_data_6-9.rds")

Visualising the dependent variable

ggplot(data = SIM_data,
       aes(x = TRIPS)) +
  geom_histogram()

SIM_data <- SIM_data %>% filter(dist > 0)
ggplot(data =SIM_data, aes(x = dist, y = TRIPS)) +
  geom_point() +
  geom_smooth(method = lm)

On the other hand, if we plot the scatter plot by using the log transformed version of both variables, we can see that their relationship is more resemble linear relationship.

ggplot(data = SIM_data,
       aes(x = log(dist),
           y = log(TRIPS))) +
  geom_point() +
  geom_smooth(method = lm)

Checking for variables with zero values

summary(SIM_data)
  ORIGIN_SZ          DESTIN_SZ             TRIPS         FlowNoIntra      
 Length:14734       Length:14734       Min.   :     1   Min.   :     0.0  
 Class :character   Class :character   1st Qu.:    14   1st Qu.:    13.0  
 Mode  :character   Mode  :character   Median :    76   Median :    70.0  
                                       Mean   :  1021   Mean   :   839.9  
                                       3rd Qu.:   426   3rd Qu.:   379.0  
                                       Max.   :232187   Max.   :148274.0  
     offset              dist       ORIGIN_AGE7_12 ORIGIN_AGE13_24
 Min.   :0.000001   Min.   :   50   Min.   :   0   Min.   :    0  
 1st Qu.:1.000000   1st Qu.: 3346   1st Qu.: 240   1st Qu.:  440  
 Median :1.000000   Median : 6067   Median : 700   Median : 1350  
 Mean   :0.982150   Mean   : 6880   Mean   :1032   Mean   : 2269  
 3rd Qu.:1.000000   3rd Qu.: 9729   3rd Qu.:1480   3rd Qu.: 3260  
 Max.   :1.000000   Max.   :26136   Max.   :6340   Max.   :16380  
 ORIGIN_AGE25_64 DESTIN_AGE7_12 DESTIN_AGE13_24 DESTIN_AGE25_64
 Min.   :    0   Min.   :   0   Min.   :    0   Min.   :    0  
 1st Qu.: 2200   1st Qu.: 240   1st Qu.:  460   1st Qu.: 2200  
 Median : 6810   Median : 720   Median : 1420   Median : 7030  
 Mean   :10487   Mean   :1033   Mean   : 2290   Mean   :10574  
 3rd Qu.:15770   3rd Qu.:1500   3rd Qu.: 3260   3rd Qu.:15830  
 Max.   :74610   Max.   :6340   Max.   :16380   Max.   :74610  

In view of this, code chunk below will be used to replace zero values to 0.99.

SIM_data$DESTIN_AGE7_12 <- ifelse(
  SIM_data$DESTIN_AGE7_12 == 0,
  0.99, SIM_data$DESTIN_AGE7_12)
SIM_data$DESTIN_AGE13_24 <- ifelse(
  SIM_data$DESTIN_AGE13_24 == 0,
  0.99, SIM_data$DESTIN_AGE13_24)
SIM_data$DESTIN_AGE25_64 <- ifelse(
  SIM_data$DESTIN_AGE25_64 == 0,
  0.99, SIM_data$DESTIN_AGE25_64)
SIM_data$ORIGIN_AGE7_12 <- ifelse(
  SIM_data$ORIGIN_AGE7_12 == 0,
  0.99, SIM_data$ORIGIN_AGE7_12)
SIM_data$ORIGIN_AGE13_24 <- ifelse(
  SIM_data$ORIGIN_AGE13_24 == 0,
  0.99, SIM_data$ORIGIN_AGE13_24)
SIM_data$ORIGIN_AGE25_64 <- ifelse(
  SIM_data$ORIGIN_AGE25_64 == 0,
  0.99, SIM_data$ORIGIN_AGE25_64)
summary(SIM_data)
  ORIGIN_SZ          DESTIN_SZ             TRIPS         FlowNoIntra      
 Length:14734       Length:14734       Min.   :     1   Min.   :     0.0  
 Class :character   Class :character   1st Qu.:    14   1st Qu.:    13.0  
 Mode  :character   Mode  :character   Median :    76   Median :    70.0  
                                       Mean   :  1021   Mean   :   839.9  
                                       3rd Qu.:   426   3rd Qu.:   379.0  
                                       Max.   :232187   Max.   :148274.0  
     offset              dist       ORIGIN_AGE7_12    ORIGIN_AGE13_24   
 Min.   :0.000001   Min.   :   50   Min.   :   0.99   Min.   :    0.99  
 1st Qu.:1.000000   1st Qu.: 3346   1st Qu.: 240.00   1st Qu.:  440.00  
 Median :1.000000   Median : 6067   Median : 700.00   Median : 1350.00  
 Mean   :0.982150   Mean   : 6880   Mean   :1031.86   Mean   : 2268.84  
 3rd Qu.:1.000000   3rd Qu.: 9729   3rd Qu.:1480.00   3rd Qu.: 3260.00  
 Max.   :1.000000   Max.   :26136   Max.   :6340.00   Max.   :16380.00  
 ORIGIN_AGE25_64    DESTIN_AGE7_12    DESTIN_AGE13_24    DESTIN_AGE25_64   
 Min.   :    0.99   Min.   :   0.99   Min.   :    0.99   Min.   :    0.99  
 1st Qu.: 2200.00   1st Qu.: 240.00   1st Qu.:  460.00   1st Qu.: 2200.00  
 Median : 6810.00   Median : 720.00   Median : 1420.00   Median : 7030.00  
 Mean   :10487.62   Mean   :1033.40   Mean   : 2290.35   Mean   :10574.46  
 3rd Qu.:15770.00   3rd Qu.:1500.00   3rd Qu.: 3260.00   3rd Qu.:15830.00  
 Max.   :74610.00   Max.   :6340.00   Max.   :16380.00   Max.   :74610.00  

Unconstrained Spatial Interaction Model

uncSIM <- glm(formula = TRIPS ~ 
                log(ORIGIN_AGE25_64) + 
                log(DESTIN_AGE25_64) +
                log(dist),
              family = poisson(link = "log"),
              data = SIM_data,
              na.action = na.exclude)
uncSIM

Call:  glm(formula = TRIPS ~ log(ORIGIN_AGE25_64) + log(DESTIN_AGE25_64) + 
    log(dist), family = poisson(link = "log"), data = SIM_data, 
    na.action = na.exclude)

Coefficients:
         (Intercept)  log(ORIGIN_AGE25_64)  log(DESTIN_AGE25_64)  
           10.407308              0.244859              0.009562  
           log(dist)  
           -0.705896  

Degrees of Freedom: 14733 Total (i.e. Null);  14730 Residual
Null Deviance:      60800000 
Residual Deviance: 36430000     AIC: 36520000

R-squared function

CalcRSquared <- function(observed,estimated){
  r <- cor(observed,estimated)
  R2 <- r^2
  R2
}
CalcRSquared(uncSIM$data$TRIPS, uncSIM$fitted.values)
[1] 0.1892576
r2_mcfadden(uncSIM)
# R2 for Generalized Linear Regression
       R2: 0.400
  adj. R2: 0.400

Origin (Production) constrained SIM

orcSIM <- glm(formula = TRIPS ~ 
                 ORIGIN_SZ +
                 log(DESTIN_AGE25_64) +
                 log(dist),
              family = poisson(link = "log"),
              data = SIM_data,
              na.action = na.exclude)
summary(orcSIM)

Call:
glm(formula = TRIPS ~ ORIGIN_SZ + log(DESTIN_AGE25_64) + log(dist), 
    family = poisson(link = "log"), data = SIM_data, na.action = na.exclude)

Coefficients:
                       Estimate Std. Error   z value Pr(>|z|)    
(Intercept)           1.211e+01  3.785e-03  3199.012  < 2e-16 ***
ORIGIN_SZAMSZ02       1.008e+00  4.450e-03   226.401  < 2e-16 ***
ORIGIN_SZAMSZ03       5.474e-01  4.563e-03   119.959  < 2e-16 ***
ORIGIN_SZAMSZ04      -7.494e-02  5.187e-03   -14.448  < 2e-16 ***
ORIGIN_SZAMSZ05      -2.006e-01  5.790e-03   -34.650  < 2e-16 ***
ORIGIN_SZAMSZ06       4.193e-01  5.130e-03    81.736  < 2e-16 ***
ORIGIN_SZAMSZ07      -1.372e+00  9.683e-03  -141.686  < 2e-16 ***
ORIGIN_SZAMSZ08      -1.022e+00  8.956e-03  -114.087  < 2e-16 ***
ORIGIN_SZAMSZ09       2.239e-01  5.408e-03    41.396  < 2e-16 ***
ORIGIN_SZAMSZ10       5.061e-01  4.716e-03   107.311  < 2e-16 ***
ORIGIN_SZAMSZ11      -1.856e+00  1.285e-02  -144.414  < 2e-16 ***
ORIGIN_SZAMSZ12      -1.580e+00  1.076e-02  -146.883  < 2e-16 ***
ORIGIN_SZBDSZ01       1.072e+00  4.345e-03   246.734  < 2e-16 ***
ORIGIN_SZBDSZ02       5.198e-01  5.079e-03   102.340  < 2e-16 ***
ORIGIN_SZBDSZ03       9.865e-01  4.490e-03   219.724  < 2e-16 ***
ORIGIN_SZBDSZ04       1.767e+00  3.894e-03   453.646  < 2e-16 ***
ORIGIN_SZBDSZ05       6.395e-01  4.546e-03   140.691  < 2e-16 ***
ORIGIN_SZBDSZ06       9.363e-01  4.543e-03   206.094  < 2e-16 ***
ORIGIN_SZBDSZ07      -1.281e+00  9.558e-03  -133.991  < 2e-16 ***
ORIGIN_SZBDSZ08      -1.167e+00  9.032e-03  -129.194  < 2e-16 ***
ORIGIN_SZBKSZ01      -4.540e-01  6.538e-03   -69.437  < 2e-16 ***
ORIGIN_SZBKSZ02       3.736e-01  5.115e-03    73.050  < 2e-16 ***
ORIGIN_SZBKSZ03       5.841e-01  4.934e-03   118.375  < 2e-16 ***
ORIGIN_SZBKSZ04      -1.177e-01  5.914e-03   -19.895  < 2e-16 ***
ORIGIN_SZBKSZ05      -2.164e-01  5.832e-03   -37.115  < 2e-16 ***
ORIGIN_SZBKSZ06       3.684e-03  5.873e-03     0.627  0.53048    
ORIGIN_SZBKSZ07       7.456e-01  4.426e-03   168.439  < 2e-16 ***
ORIGIN_SZBKSZ08      -2.279e-02  5.348e-03    -4.261 2.04e-05 ***
ORIGIN_SZBKSZ09      -9.572e-02  5.721e-03   -16.733  < 2e-16 ***
ORIGIN_SZBLSZ01      -1.688e+00  1.482e-02  -113.887  < 2e-16 ***
ORIGIN_SZBLSZ02      -2.154e+00  1.924e-02  -111.980  < 2e-16 ***
ORIGIN_SZBLSZ03      -3.249e+00  3.930e-02   -82.662  < 2e-16 ***
ORIGIN_SZBLSZ04      -2.203e+00  2.306e-02   -95.557  < 2e-16 ***
ORIGIN_SZBMSZ01      -1.267e-01  5.222e-03   -24.266  < 2e-16 ***
ORIGIN_SZBMSZ02      -1.075e+00  6.742e-03  -159.386  < 2e-16 ***
ORIGIN_SZBMSZ03      -4.386e-01  5.794e-03   -75.707  < 2e-16 ***
ORIGIN_SZBMSZ04      -6.333e-02  5.157e-03   -12.280  < 2e-16 ***
ORIGIN_SZBMSZ05      -2.256e+00  1.247e-02  -180.957  < 2e-16 ***
ORIGIN_SZBMSZ06      -2.378e+00  1.618e-02  -147.029  < 2e-16 ***
ORIGIN_SZBMSZ07      -4.769e-01  5.653e-03   -84.362  < 2e-16 ***
ORIGIN_SZBMSZ08      -5.652e-01  5.811e-03   -97.259  < 2e-16 ***
ORIGIN_SZBMSZ09      -1.232e+00  8.688e-03  -141.760  < 2e-16 ***
ORIGIN_SZBMSZ10      -1.471e+00  9.130e-03  -161.131  < 2e-16 ***
ORIGIN_SZBMSZ11      -7.866e-01  6.595e-03  -119.263  < 2e-16 ***
ORIGIN_SZBMSZ12      -1.072e+00  9.149e-03  -117.206  < 2e-16 ***
ORIGIN_SZBMSZ13      -1.207e-01  5.691e-03   -21.218  < 2e-16 ***
ORIGIN_SZBMSZ14      -5.376e-01  6.629e-03   -81.098  < 2e-16 ***
ORIGIN_SZBMSZ15      -3.253e-01  6.054e-03   -53.740  < 2e-16 ***
ORIGIN_SZBMSZ16      -1.548e+00  9.144e-03  -169.303  < 2e-16 ***
ORIGIN_SZBMSZ17      -2.169e+00  1.576e-02  -137.622  < 2e-16 ***
ORIGIN_SZBPSZ01       1.369e-01  5.553e-03    24.660  < 2e-16 ***
ORIGIN_SZBPSZ02      -3.292e-02  6.462e-03    -5.094 3.50e-07 ***
ORIGIN_SZBPSZ03       1.491e-01  6.149e-03    24.241  < 2e-16 ***
ORIGIN_SZBPSZ04       3.544e-01  5.084e-03    69.711  < 2e-16 ***
ORIGIN_SZBPSZ05       5.454e-01  4.554e-03   119.764  < 2e-16 ***
ORIGIN_SZBPSZ06      -1.406e+00  9.311e-03  -151.045  < 2e-16 ***
ORIGIN_SZBPSZ07      -1.004e+00  8.575e-03  -117.068  < 2e-16 ***
ORIGIN_SZBSSZ01      -1.625e-02  5.276e-03    -3.080  0.00207 ** 
ORIGIN_SZBSSZ02       3.088e-01  4.787e-03    64.495  < 2e-16 ***
ORIGIN_SZBSSZ03       2.555e-01  4.689e-03    54.487  < 2e-16 ***
ORIGIN_SZBTSZ01      -6.646e-02  5.385e-03   -12.340  < 2e-16 ***
ORIGIN_SZBTSZ02      -1.078e+00  7.797e-03  -138.225  < 2e-16 ***
ORIGIN_SZBTSZ03      -2.284e-01  5.727e-03   -39.876  < 2e-16 ***
ORIGIN_SZBTSZ04      -1.053e+00  1.019e-02  -103.339  < 2e-16 ***
ORIGIN_SZBTSZ05      -1.647e+00  1.100e-02  -149.690  < 2e-16 ***
ORIGIN_SZBTSZ06      -7.804e-01  7.181e-03  -108.682  < 2e-16 ***
ORIGIN_SZBTSZ07      -2.298e+00  1.321e-02  -173.921  < 2e-16 ***
ORIGIN_SZBTSZ08      -1.283e+00  9.394e-03  -136.560  < 2e-16 ***
ORIGIN_SZCBSZ01      -1.911e+00  5.483e-02   -34.844  < 2e-16 ***
ORIGIN_SZCCSZ01      -1.758e+00  1.331e-02  -132.099  < 2e-16 ***
ORIGIN_SZCHSZ01      -1.236e+00  1.178e-02  -104.954  < 2e-16 ***
ORIGIN_SZCHSZ02      -5.424e-01  7.940e-03   -68.307  < 2e-16 ***
ORIGIN_SZCHSZ03       4.332e-01  5.841e-03    74.153  < 2e-16 ***
ORIGIN_SZCKSZ01       1.843e-01  5.117e-03    36.007  < 2e-16 ***
ORIGIN_SZCKSZ02       6.800e-01  5.087e-03   133.672  < 2e-16 ***
ORIGIN_SZCKSZ03       8.030e-01  4.522e-03   177.574  < 2e-16 ***
ORIGIN_SZCKSZ04       1.298e+00  4.562e-03   284.446  < 2e-16 ***
ORIGIN_SZCKSZ05       1.011e+00  5.305e-03   190.602  < 2e-16 ***
ORIGIN_SZCKSZ06       1.262e+00  5.042e-03   250.262  < 2e-16 ***
ORIGIN_SZCLSZ01      -6.805e-01  7.661e-03   -88.836  < 2e-16 ***
ORIGIN_SZCLSZ02      -1.837e+00  1.364e-02  -134.665  < 2e-16 ***
ORIGIN_SZCLSZ03      -1.001e+00  7.949e-03  -125.969  < 2e-16 ***
ORIGIN_SZCLSZ04       6.966e-01  4.460e-03   156.204  < 2e-16 ***
ORIGIN_SZCLSZ05      -1.974e+00  1.474e-02  -133.906  < 2e-16 ***
ORIGIN_SZCLSZ06       8.585e-01  4.204e-03   204.230  < 2e-16 ***
ORIGIN_SZCLSZ07      -2.974e-01  5.575e-03   -53.346  < 2e-16 ***
ORIGIN_SZCLSZ08       3.231e-01  5.802e-03    55.688  < 2e-16 ***
ORIGIN_SZCLSZ09      -1.697e+00  1.555e-02  -109.106  < 2e-16 ***
ORIGIN_SZDTSZ02      -4.061e+00  8.341e-02   -48.693  < 2e-16 ***
ORIGIN_SZDTSZ03      -4.031e+00  7.381e-02   -54.618  < 2e-16 ***
ORIGIN_SZDTSZ13      -3.000e+00  3.129e-02   -95.889  < 2e-16 ***
ORIGIN_SZGLSZ01      -1.405e+00  9.192e-03  -152.876  < 2e-16 ***
ORIGIN_SZGLSZ02       2.536e-01  4.889e-03    51.880  < 2e-16 ***
ORIGIN_SZGLSZ03       2.411e-01  4.855e-03    49.649  < 2e-16 ***
ORIGIN_SZGLSZ04       8.350e-01  4.200e-03   198.826  < 2e-16 ***
ORIGIN_SZGLSZ05       6.207e-01  4.375e-03   141.857  < 2e-16 ***
ORIGIN_SZHGSZ01       2.806e-01  4.746e-03    59.121  < 2e-16 ***
ORIGIN_SZHGSZ02       4.917e-01  4.712e-03   104.351  < 2e-16 ***
ORIGIN_SZHGSZ03       2.452e-01  5.113e-03    47.952  < 2e-16 ***
ORIGIN_SZHGSZ04       9.052e-01  4.303e-03   210.358  < 2e-16 ***
ORIGIN_SZHGSZ05       1.170e+00  4.253e-03   275.033  < 2e-16 ***
ORIGIN_SZHGSZ06      -1.016e-01  5.413e-03   -18.773  < 2e-16 ***
ORIGIN_SZHGSZ07       6.984e-01  4.455e-03   156.757  < 2e-16 ***
ORIGIN_SZHGSZ08       1.005e-01  5.354e-03    18.781  < 2e-16 ***
ORIGIN_SZHGSZ09      -5.390e-01  6.962e-03   -77.417  < 2e-16 ***
ORIGIN_SZHGSZ10      -3.512e+00  4.211e-02   -83.388  < 2e-16 ***
ORIGIN_SZJESZ01       4.022e-01  4.869e-03    82.601  < 2e-16 ***
ORIGIN_SZJESZ02       2.273e-01  4.924e-03    46.158  < 2e-16 ***
ORIGIN_SZJESZ03       1.829e-01  5.286e-03    34.598  < 2e-16 ***
ORIGIN_SZJESZ04      -1.177e+00  9.142e-03  -128.767  < 2e-16 ***
ORIGIN_SZJESZ05      -2.065e+00  1.382e-02  -149.494  < 2e-16 ***
ORIGIN_SZJESZ06       2.301e-01  4.853e-03    47.410  < 2e-16 ***
ORIGIN_SZJESZ07      -1.889e+00  1.183e-02  -159.599  < 2e-16 ***
ORIGIN_SZJESZ08      -1.062e+00  1.147e-02   -92.551  < 2e-16 ***
ORIGIN_SZJESZ09       5.237e-01  4.959e-03   105.612  < 2e-16 ***
ORIGIN_SZJESZ10      -1.829e+00  1.800e-02  -101.616  < 2e-16 ***
ORIGIN_SZJESZ11      -2.023e+00  1.931e-02  -104.738  < 2e-16 ***
ORIGIN_SZJWSZ01       2.125e-01  6.405e-03    33.183  < 2e-16 ***
ORIGIN_SZJWSZ02       8.858e-01  4.521e-03   195.929  < 2e-16 ***
ORIGIN_SZJWSZ03       1.269e+00  4.188e-03   302.922  < 2e-16 ***
ORIGIN_SZJWSZ04       1.284e+00  4.280e-03   300.017  < 2e-16 ***
ORIGIN_SZJWSZ05      -1.393e+00  1.252e-02  -111.339  < 2e-16 ***
ORIGIN_SZJWSZ06      -1.015e+00  1.067e-02   -95.109  < 2e-16 ***
ORIGIN_SZJWSZ07      -2.694e+00  2.751e-02   -97.911  < 2e-16 ***
ORIGIN_SZJWSZ08       1.950e+00  4.110e-03   474.430  < 2e-16 ***
ORIGIN_SZJWSZ09       1.831e+00  3.899e-03   469.595  < 2e-16 ***
ORIGIN_SZKLSZ01       1.636e-01  4.902e-03    33.374  < 2e-16 ***
ORIGIN_SZKLSZ02      -5.156e-01  6.321e-03   -81.570  < 2e-16 ***
ORIGIN_SZKLSZ03      -4.145e-01  5.949e-03   -69.666  < 2e-16 ***
ORIGIN_SZKLSZ04      -2.283e+00  1.187e-02  -192.327  < 2e-16 ***
ORIGIN_SZKLSZ05      -8.593e-01  8.272e-03  -103.882  < 2e-16 ***
ORIGIN_SZKLSZ06      -4.709e+00  1.857e-01   -25.352  < 2e-16 ***
ORIGIN_SZKLSZ07      -1.123e+00  8.408e-03  -133.615  < 2e-16 ***
ORIGIN_SZKLSZ08      -1.476e+00  9.152e-03  -161.321  < 2e-16 ***
ORIGIN_SZLKSZ01      -3.273e+00  3.875e-02   -84.465  < 2e-16 ***
ORIGIN_SZMDSZ01      -2.615e+00  2.802e-02   -93.303  < 2e-16 ***
ORIGIN_SZMDSZ02      -8.945e-01  1.035e-02   -86.389  < 2e-16 ***
ORIGIN_SZMDSZ03      -1.998e+00  1.703e-02  -117.297  < 2e-16 ***
ORIGIN_SZMPSZ01      -1.093e+00  8.367e-03  -130.656  < 2e-16 ***
ORIGIN_SZMPSZ02      -5.975e-01  6.898e-03   -86.616  < 2e-16 ***
ORIGIN_SZMPSZ03      -9.706e-03  5.319e-03    -1.825  0.06804 .  
ORIGIN_SZMUSZ02      -3.923e+00  1.038e-01   -37.806  < 2e-16 ***
ORIGIN_SZNTSZ01      -2.829e+00  3.529e-02   -80.157  < 2e-16 ***
ORIGIN_SZNTSZ02      -3.256e+00  2.323e-02  -140.180  < 2e-16 ***
ORIGIN_SZNTSZ03      -9.865e-01  7.777e-03  -126.848  < 2e-16 ***
ORIGIN_SZNTSZ05      -3.353e+00  4.964e-02   -67.546  < 2e-16 ***
ORIGIN_SZNTSZ06      -3.818e+00  5.576e-02   -68.483  < 2e-16 ***
ORIGIN_SZNVSZ01       4.449e-01  4.482e-03    99.269  < 2e-16 ***
ORIGIN_SZNVSZ02      -6.279e-01  6.470e-03   -97.044  < 2e-16 ***
ORIGIN_SZNVSZ03      -1.212e+00  7.788e-03  -155.644  < 2e-16 ***
ORIGIN_SZNVSZ04      -1.469e+00  9.091e-03  -161.543  < 2e-16 ***
ORIGIN_SZNVSZ05      -2.628e+00  1.579e-02  -166.466  < 2e-16 ***
ORIGIN_SZPGSZ01      -9.541e-01  1.223e-02   -78.035  < 2e-16 ***
ORIGIN_SZPGSZ02      -5.353e-01  7.233e-03   -74.009  < 2e-16 ***
ORIGIN_SZPGSZ03       9.574e-01  4.437e-03   215.779  < 2e-16 ***
ORIGIN_SZPGSZ04       1.110e+00  4.417e-03   251.169  < 2e-16 ***
ORIGIN_SZPGSZ05       2.658e-01  5.758e-03    46.156  < 2e-16 ***
ORIGIN_SZPLSZ01      -8.153e-01  1.044e-02   -78.119  < 2e-16 ***
ORIGIN_SZPLSZ02      -1.675e+00  1.478e-02  -113.340  < 2e-16 ***
ORIGIN_SZPLSZ03      -2.963e+00  3.672e-02   -80.686  < 2e-16 ***
ORIGIN_SZPLSZ04      -3.279e+00  3.684e-02   -89.012  < 2e-16 ***
ORIGIN_SZPLSZ05      -2.466e+00  2.245e-02  -109.864  < 2e-16 ***
ORIGIN_SZPNSZ01       1.411e+00  4.584e-03   307.690  < 2e-16 ***
ORIGIN_SZPNSZ02      -5.043e-01  1.108e-02   -45.503  < 2e-16 ***
ORIGIN_SZPNSZ03      -1.878e+00  1.940e-02   -96.796  < 2e-16 ***
ORIGIN_SZPNSZ04      -2.761e+00  3.112e-02   -88.706  < 2e-16 ***
ORIGIN_SZPNSZ05      -2.277e+00  2.628e-02   -86.662  < 2e-16 ***
ORIGIN_SZPRSZ01      -7.934e-01  1.142e-02   -69.499  < 2e-16 ***
ORIGIN_SZPRSZ02       9.414e-01  4.615e-03   203.981  < 2e-16 ***
ORIGIN_SZPRSZ03       7.674e-01  4.626e-03   165.881  < 2e-16 ***
ORIGIN_SZPRSZ04      -3.771e-01  7.516e-03   -50.168  < 2e-16 ***
ORIGIN_SZPRSZ05       1.327e+00  4.325e-03   306.737  < 2e-16 ***
ORIGIN_SZPRSZ06      -4.081e-01  8.651e-03   -47.172  < 2e-16 ***
ORIGIN_SZPRSZ07      -2.151e+00  1.610e-02  -133.558  < 2e-16 ***
ORIGIN_SZPRSZ08       5.293e-04  6.383e-03     0.083  0.93391    
ORIGIN_SZQTSZ01      -4.144e-01  6.846e-03   -60.539  < 2e-16 ***
ORIGIN_SZQTSZ02      -7.967e-01  6.327e-03  -125.933  < 2e-16 ***
ORIGIN_SZQTSZ03      -2.415e-01  5.681e-03   -42.509  < 2e-16 ***
ORIGIN_SZQTSZ04      -1.013e+00  7.129e-03  -142.123  < 2e-16 ***
ORIGIN_SZQTSZ05      -3.923e-01  5.994e-03   -65.446  < 2e-16 ***
ORIGIN_SZQTSZ06      -5.662e-01  6.481e-03   -87.359  < 2e-16 ***
ORIGIN_SZQTSZ07      -1.558e+00  9.635e-03  -161.662  < 2e-16 ***
ORIGIN_SZQTSZ08      -1.577e-01  5.699e-03   -27.665  < 2e-16 ***
ORIGIN_SZQTSZ09      -6.189e-01  6.633e-03   -93.312  < 2e-16 ***
ORIGIN_SZQTSZ10      -4.511e-01  6.512e-03   -69.271  < 2e-16 ***
ORIGIN_SZQTSZ11      -1.455e+00  9.800e-03  -148.421  < 2e-16 ***
ORIGIN_SZQTSZ12      -1.475e+00  1.044e-02  -141.309  < 2e-16 ***
ORIGIN_SZQTSZ13      -3.529e-01  6.413e-03   -55.038  < 2e-16 ***
ORIGIN_SZQTSZ14      -1.591e+00  9.847e-03  -161.565  < 2e-16 ***
ORIGIN_SZQTSZ15      -8.955e-01  1.027e-02   -87.184  < 2e-16 ***
ORIGIN_SZRCSZ01      -1.375e+00  1.265e-02  -108.704  < 2e-16 ***
ORIGIN_SZRCSZ06      -6.196e-01  8.475e-03   -73.116  < 2e-16 ***
ORIGIN_SZRVSZ01      -3.523e+00  3.237e-02  -108.818  < 2e-16 ***
ORIGIN_SZRVSZ02      -2.912e+00  2.776e-02  -104.868  < 2e-16 ***
ORIGIN_SZRVSZ03      -3.145e+00  2.379e-02  -132.232  < 2e-16 ***
ORIGIN_SZRVSZ04      -3.357e+00  5.567e-02   -60.309  < 2e-16 ***
ORIGIN_SZRVSZ05      -2.438e+00  1.644e-02  -148.272  < 2e-16 ***
ORIGIN_SZSBSZ01       5.890e-01  5.529e-03   106.520  < 2e-16 ***
ORIGIN_SZSBSZ02      -7.098e-01  8.213e-03   -86.432  < 2e-16 ***
ORIGIN_SZSBSZ03       9.634e-01  4.611e-03   208.943  < 2e-16 ***
ORIGIN_SZSBSZ04       7.729e-01  5.289e-03   146.136  < 2e-16 ***
ORIGIN_SZSBSZ05      -9.966e-02  6.543e-03   -15.231  < 2e-16 ***
ORIGIN_SZSBSZ06      -1.778e+00  1.719e-02  -103.427  < 2e-16 ***
ORIGIN_SZSBSZ07      -1.161e+00  1.256e-02   -92.436  < 2e-16 ***
ORIGIN_SZSBSZ08      -1.212e+00  1.222e-02   -99.227  < 2e-16 ***
ORIGIN_SZSBSZ09      -5.783e-01  8.579e-03   -67.412  < 2e-16 ***
ORIGIN_SZSESZ02       9.999e-01  4.409e-03   226.798  < 2e-16 ***
ORIGIN_SZSESZ03       1.214e+00  4.164e-03   291.675  < 2e-16 ***
ORIGIN_SZSESZ04       8.141e-01  4.868e-03   167.238  < 2e-16 ***
ORIGIN_SZSESZ05      -2.186e-01  5.915e-03   -36.961  < 2e-16 ***
ORIGIN_SZSESZ06       7.298e-01  4.689e-03   155.641  < 2e-16 ***
ORIGIN_SZSESZ07      -2.543e+00  1.961e-02  -129.689  < 2e-16 ***
ORIGIN_SZSGSZ01      -1.016e+00  8.550e-03  -118.869  < 2e-16 ***
ORIGIN_SZSGSZ02      -1.120e+00  9.589e-03  -116.799  < 2e-16 ***
ORIGIN_SZSGSZ03       2.169e-01  5.167e-03    41.970  < 2e-16 ***
ORIGIN_SZSGSZ04       2.672e-01  4.792e-03    55.757  < 2e-16 ***
ORIGIN_SZSGSZ05      -1.785e+00  1.060e-02  -168.456  < 2e-16 ***
ORIGIN_SZSGSZ06       4.017e-01  4.541e-03    88.470  < 2e-16 ***
ORIGIN_SZSGSZ07      -6.303e-01  6.235e-03  -101.098  < 2e-16 ***
ORIGIN_SZSKSZ01      -1.928e-01  7.765e-03   -24.826  < 2e-16 ***
ORIGIN_SZSKSZ02       3.870e-01  5.689e-03    68.026  < 2e-16 ***
ORIGIN_SZSKSZ03      -6.815e-01  7.983e-03   -85.369  < 2e-16 ***
ORIGIN_SZSKSZ04      -2.528e+00  2.702e-02   -93.548  < 2e-16 ***
ORIGIN_SZSKSZ05      -1.370e+00  1.552e-02   -88.311  < 2e-16 ***
ORIGIN_SZSLSZ01      -3.218e+00  3.058e-02  -105.238  < 2e-16 ***
ORIGIN_SZSLSZ04      -6.800e-01  7.683e-03   -88.497  < 2e-16 ***
ORIGIN_SZSRSZ01      -2.389e+00  1.583e-02  -150.989  < 2e-16 ***
ORIGIN_SZTHSZ01      -2.183e+00  4.887e-02   -44.666  < 2e-16 ***
ORIGIN_SZTHSZ03      -2.243e+00  2.243e-02  -100.025  < 2e-16 ***
ORIGIN_SZTHSZ04      -2.005e+00  2.869e-02   -69.879  < 2e-16 ***
ORIGIN_SZTHSZ06      -2.276e+00  1.784e-02  -127.557  < 2e-16 ***
ORIGIN_SZTMSZ01       4.015e-01  5.814e-03    69.048  < 2e-16 ***
ORIGIN_SZTMSZ02       2.222e+00  3.795e-03   585.568  < 2e-16 ***
ORIGIN_SZTMSZ03       1.412e+00  4.108e-03   343.608  < 2e-16 ***
ORIGIN_SZTMSZ04       9.106e-01  4.742e-03   192.036  < 2e-16 ***
ORIGIN_SZTMSZ05      -3.259e-01  7.534e-03   -43.253  < 2e-16 ***
ORIGIN_SZTNSZ01      -1.806e+00  1.038e-02  -174.076  < 2e-16 ***
ORIGIN_SZTNSZ02      -1.741e+00  9.778e-03  -178.108  < 2e-16 ***
ORIGIN_SZTNSZ03      -2.277e+00  1.338e-02  -170.199  < 2e-16 ***
ORIGIN_SZTNSZ04      -7.703e-01  7.197e-03  -107.032  < 2e-16 ***
ORIGIN_SZTPSZ01      -6.466e-01  6.287e-03  -102.841  < 2e-16 ***
ORIGIN_SZTPSZ02       4.633e-01  4.347e-03   106.578  < 2e-16 ***
ORIGIN_SZTPSZ03      -5.186e-01  6.085e-03   -85.234  < 2e-16 ***
ORIGIN_SZTPSZ04      -2.900e-01  5.779e-03   -50.190  < 2e-16 ***
ORIGIN_SZTPSZ05      -2.169e-01  6.072e-03   -35.720  < 2e-16 ***
ORIGIN_SZTPSZ06       3.357e-01  5.942e-03    56.486  < 2e-16 ***
ORIGIN_SZTPSZ07      -2.517e-01  6.317e-03   -39.846  < 2e-16 ***
ORIGIN_SZTPSZ08      -1.075e+00  9.109e-03  -118.034  < 2e-16 ***
ORIGIN_SZTPSZ09      -3.708e-01  6.189e-03   -59.903  < 2e-16 ***
ORIGIN_SZTPSZ10      -6.889e-01  7.634e-03   -90.229  < 2e-16 ***
ORIGIN_SZTPSZ11       7.661e-02  5.459e-03    14.033  < 2e-16 ***
ORIGIN_SZTPSZ12      -5.971e-01  6.522e-03   -91.552  < 2e-16 ***
ORIGIN_SZTSSZ01      -3.517e+00  4.739e-02   -74.210  < 2e-16 ***
ORIGIN_SZTSSZ02       3.022e-01  7.334e-03    41.203  < 2e-16 ***
ORIGIN_SZTSSZ03       3.730e-01  7.073e-03    52.733  < 2e-16 ***
ORIGIN_SZTSSZ04       3.610e-01  7.463e-03    48.372  < 2e-16 ***
ORIGIN_SZTSSZ05      -1.103e+00  1.404e-02   -78.566  < 2e-16 ***
ORIGIN_SZTSSZ06      -1.310e+00  1.718e-02   -76.286  < 2e-16 ***
ORIGIN_SZWCSZ01      -1.233e-01  7.861e-03   -15.690  < 2e-16 ***
ORIGIN_SZWCSZ02      -2.872e+00  3.159e-02   -90.911  < 2e-16 ***
ORIGIN_SZWCSZ03      -4.138e+00  1.241e-01   -33.349  < 2e-16 ***
ORIGIN_SZWDSZ01       1.370e+00  4.146e-03   330.448  < 2e-16 ***
ORIGIN_SZWDSZ02       1.041e+00  4.747e-03   219.219  < 2e-16 ***
ORIGIN_SZWDSZ03       2.189e+00  4.035e-03   542.344  < 2e-16 ***
ORIGIN_SZWDSZ04       1.142e+00  4.963e-03   230.074  < 2e-16 ***
ORIGIN_SZWDSZ05       5.160e-01  4.998e-03   103.230  < 2e-16 ***
ORIGIN_SZWDSZ06       1.208e+00  4.611e-03   262.019  < 2e-16 ***
ORIGIN_SZWDSZ07      -3.805e-01  8.034e-03   -47.365  < 2e-16 ***
ORIGIN_SZWDSZ08      -4.839e-01  7.878e-03   -61.426  < 2e-16 ***
ORIGIN_SZWDSZ09       1.475e+00  4.401e-03   335.097  < 2e-16 ***
ORIGIN_SZYSSZ01      -1.552e-01  5.643e-03   -27.496  < 2e-16 ***
ORIGIN_SZYSSZ02       8.958e-01  4.973e-03   180.144  < 2e-16 ***
ORIGIN_SZYSSZ03       1.757e+00  4.275e-03   411.050  < 2e-16 ***
ORIGIN_SZYSSZ04       8.439e-01  4.538e-03   185.955  < 2e-16 ***
ORIGIN_SZYSSZ05      -9.995e-02  5.920e-03   -16.884  < 2e-16 ***
ORIGIN_SZYSSZ06      -1.175e+00  1.079e-02  -108.835  < 2e-16 ***
ORIGIN_SZYSSZ07      -1.202e+00  1.127e-02  -106.642  < 2e-16 ***
ORIGIN_SZYSSZ08       1.244e-02  6.104e-03     2.039  0.04148 *  
ORIGIN_SZYSSZ09       1.385e+00  4.239e-03   326.757  < 2e-16 ***
log(DESTIN_AGE25_64)  2.298e-02  8.832e-05   260.146  < 2e-16 ***
log(dist)            -6.947e-01  1.295e-04 -5363.438  < 2e-16 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

(Dispersion parameter for poisson family taken to be 1)

    Null deviance: 60796037  on 14733  degrees of freedom
Residual deviance: 26726668  on 14453  degrees of freedom
AIC: 26818857

Number of Fisher Scoring iterations: 7
CalcRSquared(orcSIM$data$TRIPS, orcSIM$fitted.values)
[1] 0.4165837

Destination constrained

decSIM <- glm(formula = TRIPS ~ 
                DESTIN_SZ + 
                log(ORIGIN_AGE25_64) + 
                log(dist),
              family = poisson(link = "log"),
              data = SIM_data,
              na.action = na.exclude)
summary(decSIM)

Call:
glm(formula = TRIPS ~ DESTIN_SZ + log(ORIGIN_AGE25_64) + log(dist), 
    family = poisson(link = "log"), data = SIM_data, na.action = na.exclude)

Coefficients:
                       Estimate Std. Error   z value Pr(>|z|)    
(Intercept)          10.8110189  0.0033476  3229.499  < 2e-16 ***
DESTIN_SZAMSZ02       0.1775885  0.0041530    42.761  < 2e-16 ***
DESTIN_SZAMSZ03       0.2064091  0.0040888    50.482  < 2e-16 ***
DESTIN_SZAMSZ04      -0.9406455  0.0060637  -155.127  < 2e-16 ***
DESTIN_SZAMSZ05      -1.1578100  0.0061804  -187.337  < 2e-16 ***
DESTIN_SZAMSZ06      -0.8861493  0.0059241  -149.584  < 2e-16 ***
DESTIN_SZAMSZ07      -1.7712447  0.0096070  -184.370  < 2e-16 ***
DESTIN_SZAMSZ08      -1.0707197  0.0067763  -158.009  < 2e-16 ***
DESTIN_SZAMSZ09      -0.9682250  0.0060435  -160.210  < 2e-16 ***
DESTIN_SZAMSZ10       0.2612773  0.0043738    59.737  < 2e-16 ***
DESTIN_SZAMSZ11      -0.3714704  0.0086200   -43.094  < 2e-16 ***
DESTIN_SZAMSZ12       0.0250455  0.0049850     5.024 5.06e-07 ***
DESTIN_SZBDSZ01       0.5154763  0.0037827   136.271  < 2e-16 ***
DESTIN_SZBDSZ02      -0.2843120  0.0049517   -57.417  < 2e-16 ***
DESTIN_SZBDSZ03      -0.0134646  0.0042692    -3.154  0.00161 ** 
DESTIN_SZBDSZ04       1.0014441  0.0034463   290.582  < 2e-16 ***
DESTIN_SZBDSZ05       0.3721573  0.0038992    95.445  < 2e-16 ***
DESTIN_SZBDSZ06       0.2013935  0.0042182    47.744  < 2e-16 ***
DESTIN_SZBDSZ07      -1.0642612  0.0092942  -114.508  < 2e-16 ***
DESTIN_SZBDSZ08      -1.7769370  0.0105721  -168.077  < 2e-16 ***
DESTIN_SZBKSZ01      -1.1944766  0.0065580  -182.141  < 2e-16 ***
DESTIN_SZBKSZ02      -0.2604946  0.0052044   -50.053  < 2e-16 ***
DESTIN_SZBKSZ03      -0.5905775  0.0055618  -106.184  < 2e-16 ***
DESTIN_SZBKSZ04      -0.0521573  0.0048274   -10.804  < 2e-16 ***
DESTIN_SZBKSZ05      -0.8258599  0.0057094  -144.650  < 2e-16 ***
DESTIN_SZBKSZ06      -0.8696763  0.0060934  -142.725  < 2e-16 ***
DESTIN_SZBKSZ07       0.2216292  0.0040334    54.949  < 2e-16 ***
DESTIN_SZBKSZ08      -1.1179375  0.0068749  -162.612  < 2e-16 ***
DESTIN_SZBKSZ09      -0.2888733  0.0049056   -58.886  < 2e-16 ***
DESTIN_SZBLSZ01      -0.4487061  0.0070226   -63.894  < 2e-16 ***
DESTIN_SZBLSZ02       0.6343096  0.0065174    97.326  < 2e-16 ***
DESTIN_SZBLSZ03       1.3492337  0.0074135   181.997  < 2e-16 ***
DESTIN_SZBLSZ04      -0.0339193  0.0131568    -2.578  0.00993 ** 
DESTIN_SZBMSZ01      -0.3497912  0.0046910   -74.567  < 2e-16 ***
DESTIN_SZBMSZ02      -0.5995634  0.0048828  -122.792  < 2e-16 ***
DESTIN_SZBMSZ03      -0.8726401  0.0056851  -153.495  < 2e-16 ***
DESTIN_SZBMSZ04      -0.5350402  0.0048888  -109.442  < 2e-16 ***
DESTIN_SZBMSZ05      -0.4981814  0.0065971   -75.515  < 2e-16 ***
DESTIN_SZBMSZ06      -2.0640198  0.0123050  -167.739  < 2e-16 ***
DESTIN_SZBMSZ07      -0.3100988  0.0045283   -68.480  < 2e-16 ***
DESTIN_SZBMSZ08      -1.2748152  0.0062622  -203.573  < 2e-16 ***
DESTIN_SZBMSZ09      -2.8056325  0.0143532  -195.471  < 2e-16 ***
DESTIN_SZBMSZ10      -1.9166407  0.0089273  -214.693  < 2e-16 ***
DESTIN_SZBMSZ11      -1.7261160  0.0079281  -217.722  < 2e-16 ***
DESTIN_SZBMSZ12      -1.1495908  0.0077721  -147.912  < 2e-16 ***
DESTIN_SZBMSZ13      -0.5428008  0.0050824  -106.799  < 2e-16 ***
DESTIN_SZBMSZ14      -1.1422302  0.0076325  -149.653  < 2e-16 ***
DESTIN_SZBMSZ15      -1.2217517  0.0068685  -177.878  < 2e-16 ***
DESTIN_SZBMSZ16      -2.4074288  0.0107900  -223.116  < 2e-16 ***
DESTIN_SZBMSZ17      -2.6985491  0.0164771  -163.776  < 2e-16 ***
DESTIN_SZBPSZ01      -0.6183085  0.0054605  -113.233  < 2e-16 ***
DESTIN_SZBPSZ02      -1.4579175  0.0083271  -175.080  < 2e-16 ***
DESTIN_SZBPSZ03      -1.0775392  0.0075109  -143.463  < 2e-16 ***
DESTIN_SZBPSZ04      -0.6645303  0.0058070  -114.436  < 2e-16 ***
DESTIN_SZBPSZ05       0.3449386  0.0039504    87.318  < 2e-16 ***
DESTIN_SZBPSZ06      -0.9360064  0.0077394  -120.941  < 2e-16 ***
DESTIN_SZBPSZ07      -0.6850065  0.0077761   -88.091  < 2e-16 ***
DESTIN_SZBSSZ01      -0.3144210  0.0045803   -68.647  < 2e-16 ***
DESTIN_SZBSSZ02      -0.7531935  0.0051075  -147.469  < 2e-16 ***
DESTIN_SZBSSZ03       0.1964072  0.0038255    51.342  < 2e-16 ***
DESTIN_SZBTSZ01       0.0749897  0.0041584    18.033  < 2e-16 ***
DESTIN_SZBTSZ02      -0.8214254  0.0065659  -125.105  < 2e-16 ***
DESTIN_SZBTSZ03      -0.1672596  0.0047942   -34.888  < 2e-16 ***
DESTIN_SZBTSZ04      -1.7727273  0.0103706  -170.938  < 2e-16 ***
DESTIN_SZBTSZ05      -0.8162630  0.0067401  -121.105  < 2e-16 ***
DESTIN_SZBTSZ06      -0.8159130  0.0059754  -136.546  < 2e-16 ***
DESTIN_SZBTSZ07      -2.1139258  0.0105602  -200.178  < 2e-16 ***
DESTIN_SZBTSZ08      -1.3565179  0.0086828  -156.231  < 2e-16 ***
DESTIN_SZCBSZ01      -4.6643129  0.3162417   -14.749  < 2e-16 ***
DESTIN_SZCCSZ01      -1.0088833  0.0080155  -125.866  < 2e-16 ***
DESTIN_SZCHSZ01      -1.1909317  0.0095262  -125.017  < 2e-16 ***
DESTIN_SZCHSZ02       0.0890035  0.0052277    17.025  < 2e-16 ***
DESTIN_SZCHSZ03       1.4883985  0.0039094   380.724  < 2e-16 ***
DESTIN_SZCKSZ01      -0.1684738  0.0047561   -35.422  < 2e-16 ***
DESTIN_SZCKSZ02      -0.4314614  0.0051537   -83.720  < 2e-16 ***
DESTIN_SZCKSZ03       0.6413457  0.0038639   165.983  < 2e-16 ***
DESTIN_SZCKSZ04      -0.6370791  0.0059869  -106.412  < 2e-16 ***
DESTIN_SZCKSZ05      -0.4185112  0.0065348   -64.044  < 2e-16 ***
DESTIN_SZCKSZ06       0.7003888  0.0045139   155.163  < 2e-16 ***
DESTIN_SZCLSZ01       0.3751343  0.0047400    79.143  < 2e-16 ***
DESTIN_SZCLSZ02      -2.2913668  0.0133371  -171.804  < 2e-16 ***
DESTIN_SZCLSZ03      -1.0498490  0.0076548  -137.149  < 2e-16 ***
DESTIN_SZCLSZ04      -0.1118915  0.0044886   -24.928  < 2e-16 ***
DESTIN_SZCLSZ05      -1.3113032  0.0084067  -155.983  < 2e-16 ***
DESTIN_SZCLSZ06       0.1661786  0.0040203    41.334  < 2e-16 ***
DESTIN_SZCLSZ07      -0.6429895  0.0052617  -122.202  < 2e-16 ***
DESTIN_SZCLSZ08      -0.4271702  0.0057208   -74.670  < 2e-16 ***
DESTIN_SZCLSZ09       0.3882136  0.0063758    60.888  < 2e-16 ***
DESTIN_SZDTSZ02      -3.0106480  0.0348374   -86.420  < 2e-16 ***
DESTIN_SZDTSZ03      -1.4195712  0.0144110   -98.506  < 2e-16 ***
DESTIN_SZDTSZ13      -2.2368573  0.0161427  -138.567  < 2e-16 ***
DESTIN_SZGLSZ01       0.0013721  0.0051224     0.268  0.78881    
DESTIN_SZGLSZ02      -0.3376674  0.0046195   -73.097  < 2e-16 ***
DESTIN_SZGLSZ03       0.3659900  0.0038384    95.350  < 2e-16 ***
DESTIN_SZGLSZ04       0.2969928  0.0038026    78.103  < 2e-16 ***
DESTIN_SZGLSZ05       0.1786445  0.0038853    45.980  < 2e-16 ***
DESTIN_SZHGSZ01       0.2979206  0.0038825    76.735  < 2e-16 ***
DESTIN_SZHGSZ02      -0.5701034  0.0051182  -111.388  < 2e-16 ***
DESTIN_SZHGSZ03      -1.0387610  0.0061020  -170.233  < 2e-16 ***
DESTIN_SZHGSZ04      -0.2264881  0.0043617   -51.926  < 2e-16 ***
DESTIN_SZHGSZ05      -0.2287090  0.0044851   -50.993  < 2e-16 ***
DESTIN_SZHGSZ06      -0.7896437  0.0054081  -146.010  < 2e-16 ***
DESTIN_SZHGSZ07       0.2268880  0.0040336    56.249  < 2e-16 ***
DESTIN_SZHGSZ08      -0.4260784  0.0048967   -87.013  < 2e-16 ***
DESTIN_SZHGSZ09       0.1027784  0.0051341    20.019  < 2e-16 ***
DESTIN_SZHGSZ10      -2.8571803  0.0262064  -109.026  < 2e-16 ***
DESTIN_SZJESZ01      -0.0843635  0.0048222   -17.495  < 2e-16 ***
DESTIN_SZJESZ02      -0.5197682  0.0051511  -100.904  < 2e-16 ***
DESTIN_SZJESZ03      -0.6250311  0.0056619  -110.392  < 2e-16 ***
DESTIN_SZJESZ04      -0.3937360  0.0065536   -60.080  < 2e-16 ***
DESTIN_SZJESZ05      -0.9748291  0.0097665   -99.814  < 2e-16 ***
DESTIN_SZJESZ06       0.3642736  0.0040600    89.722  < 2e-16 ***
DESTIN_SZJESZ07      -1.1571882  0.0081557  -141.887  < 2e-16 ***
DESTIN_SZJESZ08      -0.5955747  0.0078071   -76.286  < 2e-16 ***
DESTIN_SZJESZ09      -0.3629500  0.0053966   -67.256  < 2e-16 ***
DESTIN_SZJESZ10       0.7691552  0.0069348   110.912  < 2e-16 ***
DESTIN_SZJESZ11       0.9365743  0.0065801   142.335  < 2e-16 ***
DESTIN_SZJWSZ01      -0.4568805  0.0064536   -70.795  < 2e-16 ***
DESTIN_SZJWSZ02      -0.2880426  0.0051632   -55.788  < 2e-16 ***
DESTIN_SZJWSZ03       0.6680404  0.0039264   170.142  < 2e-16 ***
DESTIN_SZJWSZ04       0.9492158  0.0037186   255.262  < 2e-16 ***
DESTIN_SZJWSZ05      -0.1938053  0.0060810   -31.871  < 2e-16 ***
DESTIN_SZJWSZ06       0.3813164  0.0054551    69.900  < 2e-16 ***
DESTIN_SZJWSZ07      -1.2676010  0.0280038   -45.265  < 2e-16 ***
DESTIN_SZJWSZ08       0.5013149  0.0044573   112.471  < 2e-16 ***
DESTIN_SZJWSZ09       1.4161404  0.0033937   417.291  < 2e-16 ***
DESTIN_SZKLSZ01      -0.6909444  0.0051540  -134.059  < 2e-16 ***
DESTIN_SZKLSZ02      -0.8146023  0.0057129  -142.589  < 2e-16 ***
DESTIN_SZKLSZ03      -1.3956114  0.0065167  -214.161  < 2e-16 ***
DESTIN_SZKLSZ04      -1.9070281  0.0087370  -218.270  < 2e-16 ***
DESTIN_SZKLSZ05      -0.9293576  0.0071070  -130.766  < 2e-16 ***
DESTIN_SZKLSZ06      -2.5402234  0.0362062   -70.160  < 2e-16 ***
DESTIN_SZKLSZ07      -1.2017213  0.0065751  -182.769  < 2e-16 ***
DESTIN_SZKLSZ08      -0.6083433  0.0050916  -119.480  < 2e-16 ***
DESTIN_SZLKSZ01      -1.5186810  0.0204155   -74.389  < 2e-16 ***
DESTIN_SZMDSZ01      -1.4601772  0.0198347   -73.617  < 2e-16 ***
DESTIN_SZMDSZ02      -1.1554609  0.0111345  -103.773  < 2e-16 ***
DESTIN_SZMDSZ03      -2.9919337  0.0250838  -119.277  < 2e-16 ***
DESTIN_SZMPSZ01      -1.1705809  0.0077128  -151.771  < 2e-16 ***
DESTIN_SZMPSZ02      -0.9380957  0.0060321  -155.517  < 2e-16 ***
DESTIN_SZMPSZ03      -0.1761013  0.0046389   -37.962  < 2e-16 ***
DESTIN_SZMUSZ02      -2.4525115  0.0199630  -122.853  < 2e-16 ***
DESTIN_SZNTSZ01      -3.6605524  0.0447752   -81.754  < 2e-16 ***
DESTIN_SZNTSZ02      -2.0082021  0.0108736  -184.686  < 2e-16 ***
DESTIN_SZNTSZ03      -1.2387489  0.0076141  -162.691  < 2e-16 ***
DESTIN_SZNTSZ05      -1.8054361  0.0249540   -72.351  < 2e-16 ***
DESTIN_SZNTSZ06      -2.9500517  0.0428601   -68.830  < 2e-16 ***
DESTIN_SZNVSZ01      -0.4089022  0.0044288   -92.327  < 2e-16 ***
DESTIN_SZNVSZ02      -0.6865452  0.0052770  -130.102  < 2e-16 ***
DESTIN_SZNVSZ03      -0.7333670  0.0054243  -135.199  < 2e-16 ***
DESTIN_SZNVSZ04      -2.2095097  0.0106997  -206.503  < 2e-16 ***
DESTIN_SZNVSZ05      -1.8721104  0.0089058  -210.212  < 2e-16 ***
DESTIN_SZPGSZ01      -1.8756618  0.0153008  -122.586  < 2e-16 ***
DESTIN_SZPGSZ02      -0.9435337  0.0067224  -140.356  < 2e-16 ***
DESTIN_SZPGSZ03       0.3458476  0.0040152    86.134  < 2e-16 ***
DESTIN_SZPGSZ04      -0.0271485  0.0044805    -6.059 1.37e-09 ***
DESTIN_SZPGSZ05      -0.8920273  0.0070730  -126.117  < 2e-16 ***
DESTIN_SZPLSZ01      -0.2153087  0.0068270   -31.538  < 2e-16 ***
DESTIN_SZPLSZ02      -1.3646116  0.0131155  -104.046  < 2e-16 ***
DESTIN_SZPLSZ03      -0.0869245  0.0095838    -9.070  < 2e-16 ***
DESTIN_SZPLSZ04      -0.2574560  0.0093336   -27.584  < 2e-16 ***
DESTIN_SZPLSZ05      -0.7186364  0.0116835   -61.509  < 2e-16 ***
DESTIN_SZPNSZ01       1.1326963  0.0049977   226.643  < 2e-16 ***
DESTIN_SZPNSZ02       1.6516855  0.0064492   256.106  < 2e-16 ***
DESTIN_SZPNSZ03       0.8504093  0.0077034   110.394  < 2e-16 ***
DESTIN_SZPNSZ04       1.6891381  0.0075802   222.836  < 2e-16 ***
DESTIN_SZPNSZ05       0.7402750  0.0115948    63.845  < 2e-16 ***
DESTIN_SZPRSZ01      -1.0257636  0.0084652  -121.175  < 2e-16 ***
DESTIN_SZPRSZ02      -0.2028503  0.0049839   -40.701  < 2e-16 ***
DESTIN_SZPRSZ03       0.5560483  0.0038496   144.442  < 2e-16 ***
DESTIN_SZPRSZ04      -0.6824142  0.0079047   -86.330  < 2e-16 ***
DESTIN_SZPRSZ05       0.0316117  0.0044946     7.033 2.02e-12 ***
DESTIN_SZPRSZ06       0.3706283  0.0052006    71.267  < 2e-16 ***
DESTIN_SZPRSZ07      -1.4740460  0.0117304  -125.661  < 2e-16 ***
DESTIN_SZPRSZ08      -0.7869180  0.0064862  -121.321  < 2e-16 ***
DESTIN_SZQTSZ01      -1.2790095  0.0085392  -149.781  < 2e-16 ***
DESTIN_SZQTSZ02      -1.4989188  0.0073423  -204.149  < 2e-16 ***
DESTIN_SZQTSZ03      -0.9334132  0.0064035  -145.765  < 2e-16 ***
DESTIN_SZQTSZ04      -1.0506142  0.0065335  -160.805  < 2e-16 ***
DESTIN_SZQTSZ05      -0.9765013  0.0058471  -167.006  < 2e-16 ***
DESTIN_SZQTSZ06      -1.2206088  0.0063560  -192.042  < 2e-16 ***
DESTIN_SZQTSZ07      -1.6794007  0.0108727  -154.460  < 2e-16 ***
DESTIN_SZQTSZ08      -0.1214413  0.0047980   -25.311  < 2e-16 ***
DESTIN_SZQTSZ09      -0.5252607  0.0057371   -91.555  < 2e-16 ***
DESTIN_SZQTSZ10      -0.5981644  0.0054192  -110.378  < 2e-16 ***
DESTIN_SZQTSZ11      -0.0766021  0.0053446   -14.333  < 2e-16 ***
DESTIN_SZQTSZ12      -0.6153017  0.0070680   -87.054  < 2e-16 ***
DESTIN_SZQTSZ13      -0.1690535  0.0051315   -32.944  < 2e-16 ***
DESTIN_SZQTSZ14      -0.5398362  0.0062233   -86.744  < 2e-16 ***
DESTIN_SZQTSZ15      -0.1873015  0.0073132   -25.611  < 2e-16 ***
DESTIN_SZRCSZ01      -0.5875494  0.0071798   -81.833  < 2e-16 ***
DESTIN_SZRCSZ06      -2.0856090  0.0188789  -110.473  < 2e-16 ***
DESTIN_SZRVSZ01      -2.6183708  0.0162319  -161.310  < 2e-16 ***
DESTIN_SZRVSZ02      -3.1882190  0.0326141   -97.756  < 2e-16 ***
DESTIN_SZRVSZ03      -2.5981974  0.0135074  -192.353  < 2e-16 ***
DESTIN_SZRVSZ04      -1.9741504  0.0154961  -127.396  < 2e-16 ***
DESTIN_SZRVSZ05      -3.1547734  0.0256310  -123.084  < 2e-16 ***
DESTIN_SZSBSZ01      -0.3097949  0.0060601   -51.121  < 2e-16 ***
DESTIN_SZSBSZ02      -1.1229132  0.0076338  -147.097  < 2e-16 ***
DESTIN_SZSBSZ03       0.6289715  0.0041400   151.926  < 2e-16 ***
DESTIN_SZSBSZ04       0.1419430  0.0051357    27.638  < 2e-16 ***
DESTIN_SZSBSZ05      -0.9256413  0.0071963  -128.628  < 2e-16 ***
DESTIN_SZSBSZ06      -2.3487368  0.0221611  -105.984  < 2e-16 ***
DESTIN_SZSBSZ07      -0.7864630  0.0181706   -43.282  < 2e-16 ***
DESTIN_SZSBSZ08       1.3240051  0.0051598   256.599  < 2e-16 ***
DESTIN_SZSBSZ09       0.8431156  0.0048330   174.449  < 2e-16 ***
DESTIN_SZSESZ02      -0.2385874  0.0046618   -51.180  < 2e-16 ***
DESTIN_SZSESZ03       0.5439188  0.0036932   147.276  < 2e-16 ***
DESTIN_SZSESZ04      -0.6715716  0.0054222  -123.856  < 2e-16 ***
DESTIN_SZSESZ05      -0.3601932  0.0047508   -75.818  < 2e-16 ***
DESTIN_SZSESZ06      -0.6088413  0.0057017  -106.782  < 2e-16 ***
DESTIN_SZSESZ07      -2.9477507  0.0226797  -129.973  < 2e-16 ***
DESTIN_SZSGSZ01      -0.5100640  0.0058280   -87.519  < 2e-16 ***
DESTIN_SZSGSZ02      -0.0439941  0.0051633    -8.520  < 2e-16 ***
DESTIN_SZSGSZ03      -0.3700648  0.0047152   -78.483  < 2e-16 ***
DESTIN_SZSGSZ04      -0.3021335  0.0046865   -64.468  < 2e-16 ***
DESTIN_SZSGSZ05      -2.2253287  0.0097908  -227.288  < 2e-16 ***
DESTIN_SZSGSZ06       0.2963602  0.0037948    78.097  < 2e-16 ***
DESTIN_SZSGSZ07      -0.5940373  0.0051371  -115.637  < 2e-16 ***
DESTIN_SZSISZ01      -1.4528976  0.0257790   -56.360  < 2e-16 ***
DESTIN_SZSKSZ01      -0.0374952  0.0066885    -5.606 2.07e-08 ***
DESTIN_SZSKSZ02       0.7271418  0.0050281   144.617  < 2e-16 ***
DESTIN_SZSKSZ03      -0.0640794  0.0059146   -10.834  < 2e-16 ***
DESTIN_SZSKSZ04      -0.5610767  0.0139676   -40.170  < 2e-16 ***
DESTIN_SZSKSZ05       0.1510974  0.0104871    14.408  < 2e-16 ***
DESTIN_SZSLSZ01      -0.5823031  0.0083356   -69.858  < 2e-16 ***
DESTIN_SZSLSZ04      -0.8166665  0.0070329  -116.122  < 2e-16 ***
DESTIN_SZSRSZ01      -2.3241796  0.0127215  -182.696  < 2e-16 ***
DESTIN_SZTHSZ01      -2.8157635  0.0366840   -76.757  < 2e-16 ***
DESTIN_SZTHSZ03      -2.1005978  0.0250842   -83.742  < 2e-16 ***
DESTIN_SZTHSZ04      -2.1246250  0.0213690   -99.425  < 2e-16 ***
DESTIN_SZTHSZ06      -1.4571092  0.0150031   -97.121  < 2e-16 ***
DESTIN_SZTMSZ01      -0.1234559  0.0055152   -22.385  < 2e-16 ***
DESTIN_SZTMSZ02       1.5961628  0.0032599   489.635  < 2e-16 ***
DESTIN_SZTMSZ03       0.6977233  0.0037138   187.875  < 2e-16 ***
DESTIN_SZTMSZ04       0.8606606  0.0037592   228.947  < 2e-16 ***
DESTIN_SZTMSZ05       0.3750655  0.0051281    73.140  < 2e-16 ***
DESTIN_SZTNSZ01      -1.2624562  0.0066979  -188.485  < 2e-16 ***
DESTIN_SZTNSZ02      -2.0761581  0.0096538  -215.062  < 2e-16 ***
DESTIN_SZTNSZ03      -2.1128125  0.0115717  -182.584  < 2e-16 ***
DESTIN_SZTNSZ04      -1.2417494  0.0068502  -181.271  < 2e-16 ***
DESTIN_SZTPSZ01      -0.7094356  0.0055768  -127.211  < 2e-16 ***
DESTIN_SZTPSZ02       0.1491604  0.0037260    40.032  < 2e-16 ***
DESTIN_SZTPSZ03      -0.4973355  0.0054878   -90.626  < 2e-16 ***
DESTIN_SZTPSZ04      -1.5160395  0.0071592  -211.761  < 2e-16 ***
DESTIN_SZTPSZ05      -0.9196565  0.0056750  -162.054  < 2e-16 ***
DESTIN_SZTPSZ06      -0.2710649  0.0062637   -43.276  < 2e-16 ***
DESTIN_SZTPSZ07      -2.0198681  0.0116556  -173.296  < 2e-16 ***
DESTIN_SZTPSZ08      -1.4881412  0.0085532  -173.987  < 2e-16 ***
DESTIN_SZTPSZ09      -0.5901273  0.0059394   -99.358  < 2e-16 ***
DESTIN_SZTPSZ10      -1.1215711  0.0084488  -132.749  < 2e-16 ***
DESTIN_SZTPSZ11      -0.4837089  0.0050905   -95.022  < 2e-16 ***
DESTIN_SZTPSZ12      -0.8653927  0.0061326  -141.113  < 2e-16 ***
DESTIN_SZTSSZ01      -0.5515103  0.0208541   -26.446  < 2e-16 ***
DESTIN_SZTSSZ02       0.8373778  0.0093757    89.314  < 2e-16 ***
DESTIN_SZTSSZ03       1.7021888  0.0064394   264.340  < 2e-16 ***
DESTIN_SZTSSZ04       1.5355016  0.0067855   226.292  < 2e-16 ***
DESTIN_SZTSSZ05       1.6932319  0.0073725   229.668  < 2e-16 ***
DESTIN_SZTSSZ06       0.4567808  0.0137927    33.118  < 2e-16 ***
DESTIN_SZWCSZ01       1.3967640  0.0045392   307.711  < 2e-16 ***
DESTIN_SZWCSZ02      -0.4560229  0.0122949   -37.090  < 2e-16 ***
DESTIN_SZWCSZ03      -2.0710051  0.0325121   -63.699  < 2e-16 ***
DESTIN_SZWDSZ01       1.5137342  0.0034774   435.310  < 2e-16 ***
DESTIN_SZWDSZ02      -0.3005475  0.0055149   -54.497  < 2e-16 ***
DESTIN_SZWDSZ03       1.2514543  0.0036112   346.550  < 2e-16 ***
DESTIN_SZWDSZ04      -0.1702528  0.0058295   -29.205  < 2e-16 ***
DESTIN_SZWDSZ05      -0.0005419  0.0053911    -0.101  0.91994    
DESTIN_SZWDSZ06       0.5203361  0.0040318   129.058  < 2e-16 ***
DESTIN_SZWDSZ07       0.6006472  0.0061745    97.279  < 2e-16 ***
DESTIN_SZWDSZ08       0.6650867  0.0060867   109.268  < 2e-16 ***
DESTIN_SZWDSZ09       0.6237312  0.0044830   139.132  < 2e-16 ***
DESTIN_SZYSSZ01       1.0471638  0.0038255   273.732  < 2e-16 ***
DESTIN_SZYSSZ02       0.2341114  0.0048213    48.558  < 2e-16 ***
DESTIN_SZYSSZ03      -0.0916446  0.0051335   -17.852  < 2e-16 ***
DESTIN_SZYSSZ04      -0.0085536  0.0048684    -1.757  0.07892 .  
DESTIN_SZYSSZ05      -1.5775071  0.0100297  -157.283  < 2e-16 ***
DESTIN_SZYSSZ06      -1.8130307  0.0098617  -183.846  < 2e-16 ***
DESTIN_SZYSSZ07      -1.1703963  0.0111525  -104.945  < 2e-16 ***
DESTIN_SZYSSZ08       0.5253514  0.0039556   132.813  < 2e-16 ***
DESTIN_SZYSSZ09       0.4353435  0.0038890   111.943  < 2e-16 ***
log(ORIGIN_AGE25_64)  0.2249135  0.0001404  1602.353  < 2e-16 ***
log(dist)            -0.6989356  0.0001287 -5431.279  < 2e-16 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

(Dispersion parameter for poisson family taken to be 1)

    Null deviance: 60796037  on 14733  degrees of freedom
Residual deviance: 26208384  on 14452  degrees of freedom
AIC: 26300575

Number of Fisher Scoring iterations: 7
CalcRSquared(decSIM$data$TRIPS, decSIM$fitted.values)
[1] 0.4972985

Doubly constrained

dbcSIM <- glm(formula = TRIPS ~ 
                ORIGIN_SZ + 
                DESTIN_SZ + 
                log(dist),
              family = poisson(link = "log"),
              data = SIM_data,
              na.action = na.exclude)
summary(dbcSIM)

Call:
glm(formula = TRIPS ~ ORIGIN_SZ + DESTIN_SZ + log(dist), family = poisson(link = "log"), 
    data = SIM_data, na.action = na.exclude)

Coefficients:
                  Estimate Std. Error   z value Pr(>|z|)    
(Intercept)     12.4165310  0.0043949  2825.242  < 2e-16 ***
ORIGIN_SZAMSZ02  0.9496891  0.0045740   207.630  < 2e-16 ***
ORIGIN_SZAMSZ03  0.5519174  0.0046672   118.253  < 2e-16 ***
ORIGIN_SZAMSZ04  0.1028140  0.0052468    19.596  < 2e-16 ***
ORIGIN_SZAMSZ05  0.0822549  0.0058663    14.022  < 2e-16 ***
ORIGIN_SZAMSZ06  0.6617809  0.0052580   125.861  < 2e-16 ***
ORIGIN_SZAMSZ07 -0.9508298  0.0097681   -97.340  < 2e-16 ***
ORIGIN_SZAMSZ08 -0.7271779  0.0090946   -79.958  < 2e-16 ***
ORIGIN_SZAMSZ09  0.4896781  0.0055203    88.704  < 2e-16 ***
ORIGIN_SZAMSZ10  0.4819428  0.0048175   100.040  < 2e-16 ***
ORIGIN_SZAMSZ11 -1.7719841  0.0130695  -135.582  < 2e-16 ***
ORIGIN_SZAMSZ12 -1.7679107  0.0108777  -162.526  < 2e-16 ***
ORIGIN_SZBDSZ01  0.8314812  0.0045187   184.010  < 2e-16 ***
ORIGIN_SZBDSZ02  0.4305836  0.0052535    81.961  < 2e-16 ***
ORIGIN_SZBDSZ03  0.8009370  0.0046384   172.676  < 2e-16 ***
ORIGIN_SZBDSZ04  1.4562985  0.0040456   359.971  < 2e-16 ***
ORIGIN_SZBDSZ05  0.4501939  0.0046960    95.867  < 2e-16 ***
ORIGIN_SZBDSZ06  0.7745026  0.0047424   163.314  < 2e-16 ***
ORIGIN_SZBDSZ07 -1.1784123  0.0098105  -120.117  < 2e-16 ***
ORIGIN_SZBDSZ08 -0.9830996  0.0091135  -107.873  < 2e-16 ***
ORIGIN_SZBKSZ01 -0.3042966  0.0067086   -45.359  < 2e-16 ***
ORIGIN_SZBKSZ02  0.4801541  0.0054160    88.655  < 2e-16 ***
ORIGIN_SZBKSZ03  0.7823931  0.0052007   150.440  < 2e-16 ***
ORIGIN_SZBKSZ04 -0.1292545  0.0061735   -20.937  < 2e-16 ***
ORIGIN_SZBKSZ05 -0.0258584  0.0060192    -4.296 1.74e-05 ***
ORIGIN_SZBKSZ06  0.1994719  0.0061206    32.590  < 2e-16 ***
ORIGIN_SZBKSZ07  0.7434860  0.0046598   159.553  < 2e-16 ***
ORIGIN_SZBKSZ08  0.1625007  0.0055219    29.428  < 2e-16 ***
ORIGIN_SZBKSZ09 -0.0864293  0.0059533   -14.518  < 2e-16 ***
ORIGIN_SZBLSZ01 -2.1022485  0.0150316  -139.855  < 2e-16 ***
ORIGIN_SZBLSZ02 -2.9460181  0.0195760  -150.491  < 2e-16 ***
ORIGIN_SZBLSZ03 -4.9412872  0.0398540  -123.985  < 2e-16 ***
ORIGIN_SZBLSZ04 -2.8143593  0.0239209  -117.653  < 2e-16 ***
ORIGIN_SZBMSZ01 -0.0264561  0.0053639    -4.932 8.13e-07 ***
ORIGIN_SZBMSZ02 -0.8656513  0.0068511  -126.353  < 2e-16 ***
ORIGIN_SZBMSZ03 -0.1723467  0.0059613   -28.911  < 2e-16 ***
ORIGIN_SZBMSZ04  0.2169844  0.0053578    40.499  < 2e-16 ***
ORIGIN_SZBMSZ05 -2.0252956  0.0126107  -160.602  < 2e-16 ***
ORIGIN_SZBMSZ06 -1.7642018  0.0163931  -107.619  < 2e-16 ***
ORIGIN_SZBMSZ07 -0.3271629  0.0058137   -56.274  < 2e-16 ***
ORIGIN_SZBMSZ08 -0.2533255  0.0059335   -42.694  < 2e-16 ***
ORIGIN_SZBMSZ09 -0.7712635  0.0087939   -87.704  < 2e-16 ***
ORIGIN_SZBMSZ10 -1.0098048  0.0092519  -109.145  < 2e-16 ***
ORIGIN_SZBMSZ11 -0.3816187  0.0067302   -56.702  < 2e-16 ***
ORIGIN_SZBMSZ12 -0.6666616  0.0095680   -69.676  < 2e-16 ***
ORIGIN_SZBMSZ13 -0.0076108  0.0059040    -1.289  0.19737    
ORIGIN_SZBMSZ14 -0.1682476  0.0069391   -24.246  < 2e-16 ***
ORIGIN_SZBMSZ15  0.0904585  0.0062822    14.399  < 2e-16 ***
ORIGIN_SZBMSZ16 -1.1808741  0.0092258  -127.997  < 2e-16 ***
ORIGIN_SZBMSZ17 -1.7189127  0.0158408  -108.512  < 2e-16 ***
ORIGIN_SZBPSZ01  0.4294645  0.0058051    73.980  < 2e-16 ***
ORIGIN_SZBPSZ02  0.5028906  0.0068169    73.771  < 2e-16 ***
ORIGIN_SZBPSZ03  0.6656178  0.0066126   100.658  < 2e-16 ***
ORIGIN_SZBPSZ04  0.5203612  0.0053224    97.769  < 2e-16 ***
ORIGIN_SZBPSZ05  0.5377769  0.0047907   112.256  < 2e-16 ***
ORIGIN_SZBPSZ06 -1.2327809  0.0094950  -129.835  < 2e-16 ***
ORIGIN_SZBPSZ07 -0.9035255  0.0088739  -101.818  < 2e-16 ***
ORIGIN_SZBSSZ01  0.1210027  0.0053990    22.412  < 2e-16 ***
ORIGIN_SZBSSZ02  0.4618449  0.0048641    94.951  < 2e-16 ***
ORIGIN_SZBSSZ03  0.2160739  0.0047835    45.170  < 2e-16 ***
ORIGIN_SZBTSZ01 -0.1108042  0.0055599   -19.929  < 2e-16 ***
ORIGIN_SZBTSZ02 -0.8911221  0.0079213  -112.498  < 2e-16 ***
ORIGIN_SZBTSZ03 -0.2203980  0.0059325   -37.151  < 2e-16 ***
ORIGIN_SZBTSZ04 -0.6427946  0.0105438   -60.964  < 2e-16 ***
ORIGIN_SZBTSZ05 -1.4662312  0.0111784  -131.166  < 2e-16 ***
ORIGIN_SZBTSZ06 -0.6105884  0.0073456   -83.123  < 2e-16 ***
ORIGIN_SZBTSZ07 -1.9041317  0.0132781  -143.404  < 2e-16 ***
ORIGIN_SZBTSZ08 -1.0627939  0.0095982  -110.728  < 2e-16 ***
ORIGIN_SZCBSZ01 -2.9365941  0.0548632   -53.526  < 2e-16 ***
ORIGIN_SZCCSZ01 -1.5313555  0.0134599  -113.772  < 2e-16 ***
ORIGIN_SZCHSZ01 -1.2034494  0.0119468  -100.734  < 2e-16 ***
ORIGIN_SZCHSZ02 -0.8299415  0.0081984  -101.232  < 2e-16 ***
ORIGIN_SZCHSZ03 -0.5143946  0.0061944   -83.042  < 2e-16 ***
ORIGIN_SZCKSZ01  0.2372583  0.0053612    44.255  < 2e-16 ***
ORIGIN_SZCKSZ02  0.9124836  0.0054472   167.515  < 2e-16 ***
ORIGIN_SZCKSZ03  0.7237808  0.0048401   149.539  < 2e-16 ***
ORIGIN_SZCKSZ04  1.6884022  0.0050169   336.540  < 2e-16 ***
ORIGIN_SZCKSZ05  1.3932005  0.0062346   223.464  < 2e-16 ***
ORIGIN_SZCKSZ06  1.0670053  0.0066112   161.394  < 2e-16 ***
ORIGIN_SZCLSZ01 -0.8602837  0.0079240  -108.567  < 2e-16 ***
ORIGIN_SZCLSZ02 -1.3853421  0.0137444  -100.793  < 2e-16 ***
ORIGIN_SZCLSZ03 -0.8582608  0.0081177  -105.727  < 2e-16 ***
ORIGIN_SZCLSZ04  0.7836027  0.0046427   168.782  < 2e-16 ***
ORIGIN_SZCLSZ05 -1.8121756  0.0148960  -121.655  < 2e-16 ***
ORIGIN_SZCLSZ06  0.8296870  0.0043909   188.955  < 2e-16 ***
ORIGIN_SZCLSZ07 -0.2325219  0.0057432   -40.487  < 2e-16 ***
ORIGIN_SZCLSZ08  0.2714336  0.0062625    43.342  < 2e-16 ***
ORIGIN_SZCLSZ09 -2.2223744  0.0160946  -138.082  < 2e-16 ***
ORIGIN_SZDTSZ02 -4.0704970  0.0834192   -48.796  < 2e-16 ***
ORIGIN_SZDTSZ03 -3.4529031  0.0738295   -46.769  < 2e-16 ***
ORIGIN_SZDTSZ13 -2.8301983  0.0313085   -90.397  < 2e-16 ***
ORIGIN_SZGLSZ01 -1.4674986  0.0093137  -157.563  < 2e-16 ***
ORIGIN_SZGLSZ02  0.2749369  0.0050051    54.931  < 2e-16 ***
ORIGIN_SZGLSZ03  0.0781954  0.0049748    15.718  < 2e-16 ***
ORIGIN_SZGLSZ04  0.8167797  0.0043260   188.808  < 2e-16 ***
ORIGIN_SZGLSZ05  0.5277509  0.0044879   117.595  < 2e-16 ***
ORIGIN_SZHGSZ01  0.2323885  0.0048555    47.861  < 2e-16 ***
ORIGIN_SZHGSZ02  0.5707182  0.0048256   118.268  < 2e-16 ***
ORIGIN_SZHGSZ03  0.4231170  0.0052149    81.136  < 2e-16 ***
ORIGIN_SZHGSZ04  0.9341168  0.0044128   211.681  < 2e-16 ***
ORIGIN_SZHGSZ05  1.2192790  0.0043790   278.437  < 2e-16 ***
ORIGIN_SZHGSZ06  0.0490041  0.0054961     8.916  < 2e-16 ***
ORIGIN_SZHGSZ07  0.6337041  0.0045735   138.559  < 2e-16 ***
ORIGIN_SZHGSZ08  0.0312612  0.0054684     5.717 1.09e-08 ***
ORIGIN_SZHGSZ09 -0.6985397  0.0071800   -97.289  < 2e-16 ***
ORIGIN_SZHGSZ10 -2.9958967  0.0422303   -70.942  < 2e-16 ***
ORIGIN_SZJESZ01  0.4363431  0.0051329    85.010  < 2e-16 ***
ORIGIN_SZJESZ02  0.3460900  0.0051372    67.370  < 2e-16 ***
ORIGIN_SZJESZ03  0.2928005  0.0055108    53.132  < 2e-16 ***
ORIGIN_SZJESZ04 -1.1924298  0.0093540  -127.478  < 2e-16 ***
ORIGIN_SZJESZ05 -2.0178136  0.0139479  -144.668  < 2e-16 ***
ORIGIN_SZJESZ06  0.1637633  0.0050685    32.310  < 2e-16 ***
ORIGIN_SZJESZ07 -1.8227460  0.0119383  -152.680  < 2e-16 ***
ORIGIN_SZJESZ08 -1.1556281  0.0117870   -98.043  < 2e-16 ***
ORIGIN_SZJESZ09  0.4766229  0.0052813    90.248  < 2e-16 ***
ORIGIN_SZJESZ10 -2.6868992  0.0186864  -143.789  < 2e-16 ***
ORIGIN_SZJESZ11 -3.0618150  0.0199755  -153.278  < 2e-16 ***
ORIGIN_SZJWSZ01  0.4417418  0.0068611    64.383  < 2e-16 ***
ORIGIN_SZJWSZ02  0.9738087  0.0047905   203.281  < 2e-16 ***
ORIGIN_SZJWSZ03  1.1548028  0.0045180   255.599  < 2e-16 ***
ORIGIN_SZJWSZ04  0.9078417  0.0046668   194.532  < 2e-16 ***
ORIGIN_SZJWSZ05 -1.7092500  0.0127422  -134.141  < 2e-16 ***
ORIGIN_SZJWSZ06 -1.3284287  0.0109785  -121.002  < 2e-16 ***
ORIGIN_SZJWSZ07 -2.3231549  0.0281427   -82.549  < 2e-16 ***
ORIGIN_SZJWSZ08  1.9386127  0.0046041   421.059  < 2e-16 ***
ORIGIN_SZJWSZ09  1.3987549  0.0042610   328.266  < 2e-16 ***
ORIGIN_SZKLSZ01  0.2617735  0.0050089    52.261  < 2e-16 ***
ORIGIN_SZKLSZ02 -0.4325093  0.0064279   -67.286  < 2e-16 ***
ORIGIN_SZKLSZ03 -0.2787173  0.0060380   -46.161  < 2e-16 ***
ORIGIN_SZKLSZ04 -1.9432693  0.0119163  -163.076  < 2e-16 ***
ORIGIN_SZKLSZ05 -0.5420067  0.0085529   -63.371  < 2e-16 ***
ORIGIN_SZKLSZ06 -4.2949009  0.1857686   -23.120  < 2e-16 ***
ORIGIN_SZKLSZ07 -0.8576946  0.0085178  -100.694  < 2e-16 ***
ORIGIN_SZKLSZ08 -1.3840925  0.0092323  -149.918  < 2e-16 ***
ORIGIN_SZLKSZ01 -2.8108510  0.0392356   -71.640  < 2e-16 ***
ORIGIN_SZMDSZ01 -1.6745388  0.0296543   -56.469  < 2e-16 ***
ORIGIN_SZMDSZ02 -0.8193738  0.0106631   -76.842  < 2e-16 ***
ORIGIN_SZMDSZ03 -1.5088267  0.0172032   -87.706  < 2e-16 ***
ORIGIN_SZMPSZ01 -0.9860154  0.0085053  -115.929  < 2e-16 ***
ORIGIN_SZMPSZ02 -0.5958875  0.0070097   -85.008  < 2e-16 ***
ORIGIN_SZMPSZ03 -0.0490122  0.0054582    -8.980  < 2e-16 ***
ORIGIN_SZMUSZ02 -3.5233367  0.1037749   -33.952  < 2e-16 ***
ORIGIN_SZNTSZ01 -2.6451541  0.0353125   -74.907  < 2e-16 ***
ORIGIN_SZNTSZ02 -2.7710546  0.0232841  -119.011  < 2e-16 ***
ORIGIN_SZNTSZ03 -0.6123404  0.0079083   -77.430  < 2e-16 ***
ORIGIN_SZNTSZ05 -2.9257445  0.0496704   -58.903  < 2e-16 ***
ORIGIN_SZNTSZ06 -3.3260031  0.0557966   -59.609  < 2e-16 ***
ORIGIN_SZNVSZ01  0.6421306  0.0046037   139.482  < 2e-16 ***
ORIGIN_SZNVSZ02 -0.4251550  0.0065890   -64.525  < 2e-16 ***
ORIGIN_SZNVSZ03 -1.0765622  0.0078766  -136.679  < 2e-16 ***
ORIGIN_SZNVSZ04 -1.2289504  0.0091468  -134.358  < 2e-16 ***
ORIGIN_SZNVSZ05 -2.3551389  0.0158219  -148.853  < 2e-16 ***
ORIGIN_SZPGSZ01  0.1518212  0.0154825     9.806  < 2e-16 ***
ORIGIN_SZPGSZ02 -0.4062609  0.0073780   -55.064  < 2e-16 ***
ORIGIN_SZPGSZ03  0.8976913  0.0046122   194.636  < 2e-16 ***
ORIGIN_SZPGSZ04  1.1161685  0.0045850   243.437  < 2e-16 ***
ORIGIN_SZPGSZ05  0.4794249  0.0060213    79.621  < 2e-16 ***
ORIGIN_SZPLSZ01 -0.8322377  0.0107898   -77.132  < 2e-16 ***
ORIGIN_SZPLSZ02 -1.2968937  0.0149841   -86.551  < 2e-16 ***
ORIGIN_SZPLSZ03 -3.2744991  0.0374541   -87.427  < 2e-16 ***
ORIGIN_SZPLSZ04 -3.5423615  0.0372570   -95.079  < 2e-16 ***
ORIGIN_SZPLSZ05 -2.4343705  0.0227807  -106.861  < 2e-16 ***
ORIGIN_SZPNSZ01  0.8052461  0.0056124   143.476  < 2e-16 ***
ORIGIN_SZPNSZ02 -1.8042362  0.0128222  -140.712  < 2e-16 ***
ORIGIN_SZPNSZ03 -2.6363996  0.0200058  -131.782  < 2e-16 ***
ORIGIN_SZPNSZ04 -4.8427070  0.0320126  -151.275  < 2e-16 ***
ORIGIN_SZPNSZ05 -3.6613775  0.0285686  -128.161  < 2e-16 ***
ORIGIN_SZPRSZ01 -0.5645384  0.0117126   -48.199  < 2e-16 ***
ORIGIN_SZPRSZ02  0.9145886  0.0048137   189.998  < 2e-16 ***
ORIGIN_SZPRSZ03  0.4478971  0.0048102    93.113  < 2e-16 ***
ORIGIN_SZPRSZ04 -0.5312444  0.0079019   -67.230  < 2e-16 ***
ORIGIN_SZPRSZ05  1.1462662  0.0045250   253.318  < 2e-16 ***
ORIGIN_SZPRSZ06 -0.7392744  0.0090347   -81.826  < 2e-16 ***
ORIGIN_SZPRSZ07 -2.1667862  0.0162528  -133.318  < 2e-16 ***
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ORIGIN_SZQTSZ01  0.1062151  0.0071538    14.847  < 2e-16 ***
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ORIGIN_SZQTSZ03  0.1161844  0.0058822    19.752  < 2e-16 ***
ORIGIN_SZQTSZ04 -0.8102612  0.0072742  -111.389  < 2e-16 ***
ORIGIN_SZQTSZ05 -0.0417272  0.0061917    -6.739 1.59e-11 ***
ORIGIN_SZQTSZ06 -0.2521417  0.0066449   -37.945  < 2e-16 ***
ORIGIN_SZQTSZ07 -1.2395975  0.0097496  -127.143  < 2e-16 ***
ORIGIN_SZQTSZ08 -0.1105467  0.0059364   -18.622  < 2e-16 ***
ORIGIN_SZQTSZ09 -0.5078461  0.0067895   -74.798  < 2e-16 ***
ORIGIN_SZQTSZ10 -0.3866593  0.0066995   -57.714  < 2e-16 ***
ORIGIN_SZQTSZ11 -1.5264609  0.0099770  -152.998  < 2e-16 ***
ORIGIN_SZQTSZ12 -1.3866518  0.0106887  -129.730  < 2e-16 ***
ORIGIN_SZQTSZ13 -0.3764286  0.0066707   -56.430  < 2e-16 ***
ORIGIN_SZQTSZ14 -1.4907399  0.0100120  -148.896  < 2e-16 ***
ORIGIN_SZQTSZ15 -1.0552239  0.0108792   -96.994  < 2e-16 ***
ORIGIN_SZRCSZ01 -1.3136074  0.0126986  -103.445  < 2e-16 ***
ORIGIN_SZRCSZ06 -0.2418276  0.0085509   -28.281  < 2e-16 ***
ORIGIN_SZRVSZ01 -2.9263747  0.0324968   -90.051  < 2e-16 ***
ORIGIN_SZRVSZ02 -2.2980940  0.0278202   -82.605  < 2e-16 ***
ORIGIN_SZRVSZ03 -2.4663765  0.0238674  -103.336  < 2e-16 ***
ORIGIN_SZRVSZ04 -3.1853677  0.0556939   -57.194  < 2e-16 ***
ORIGIN_SZRVSZ05 -1.5695490  0.0166684   -94.163  < 2e-16 ***
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ORIGIN_SZSBSZ02 -0.7307279  0.0084105   -86.883  < 2e-16 ***
ORIGIN_SZSBSZ03  0.5920074  0.0050167   118.008  < 2e-16 ***
ORIGIN_SZSBSZ04  0.3684857  0.0058575    62.908  < 2e-16 ***
ORIGIN_SZSBSZ05 -0.0036863  0.0068459    -0.538  0.59026    
ORIGIN_SZSBSZ06 -1.1939284  0.0181541   -65.766  < 2e-16 ***
ORIGIN_SZSBSZ07 -0.4896579  0.0135618   -36.106  < 2e-16 ***
ORIGIN_SZSBSZ08 -2.1221691  0.0127258  -166.762  < 2e-16 ***
ORIGIN_SZSBSZ09 -1.2032410  0.0089611  -134.273  < 2e-16 ***
ORIGIN_SZSESZ02  1.0721820  0.0045336   236.498  < 2e-16 ***
ORIGIN_SZSESZ03  1.0808012  0.0042923   251.801  < 2e-16 ***
ORIGIN_SZSESZ04  1.0137448  0.0050668   200.076  < 2e-16 ***
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ORIGIN_SZSESZ06  0.9165834  0.0048323   189.677  < 2e-16 ***
ORIGIN_SZSESZ07 -2.2499789  0.0196327  -114.603  < 2e-16 ***
ORIGIN_SZSGSZ01 -0.9369800  0.0087282  -107.351  < 2e-16 ***
ORIGIN_SZSGSZ02 -1.1690716  0.0097131  -120.360  < 2e-16 ***
ORIGIN_SZSGSZ03  0.2604352  0.0052709    49.410  < 2e-16 ***
ORIGIN_SZSGSZ04  0.3468823  0.0048897    70.942  < 2e-16 ***
ORIGIN_SZSGSZ05 -1.5927797  0.0106308  -149.827  < 2e-16 ***
ORIGIN_SZSGSZ06  0.3605651  0.0046361    77.774  < 2e-16 ***
ORIGIN_SZSGSZ07 -0.5333873  0.0063119   -84.504  < 2e-16 ***
ORIGIN_SZSKSZ01 -0.2706750  0.0082836   -32.676  < 2e-16 ***
ORIGIN_SZSKSZ02  0.0970953  0.0063378    15.320  < 2e-16 ***
ORIGIN_SZSKSZ03 -0.6954342  0.0082538   -84.256  < 2e-16 ***
ORIGIN_SZSKSZ04 -2.3863580  0.0284607   -83.847  < 2e-16 ***
ORIGIN_SZSKSZ05 -1.5443140  0.0179059   -86.246  < 2e-16 ***
ORIGIN_SZSLSZ01 -2.9450656  0.0307283   -95.842  < 2e-16 ***
ORIGIN_SZSLSZ04 -0.5739349  0.0077851   -73.722  < 2e-16 ***
ORIGIN_SZSRSZ01 -1.6136735  0.0160199  -100.729  < 2e-16 ***
ORIGIN_SZTHSZ01 -2.6034976  0.0489378   -53.200  < 2e-16 ***
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ORIGIN_SZTHSZ04 -2.0110399  0.0287527   -69.943  < 2e-16 ***
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ORIGIN_SZTMSZ03  1.0941176  0.0042911   254.976  < 2e-16 ***
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ORIGIN_SZTPSZ02  0.5315265  0.0044497   119.451  < 2e-16 ***
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ORIGIN_SZTSSZ02 -0.0386819  0.0094886    -4.077 4.57e-05 ***
ORIGIN_SZTSSZ03 -0.3862387  0.0095139   -40.597  < 2e-16 ***
ORIGIN_SZTSSZ04 -0.6380676  0.0099905   -63.867  < 2e-16 ***
ORIGIN_SZTSSZ05 -2.7354613  0.0162414  -168.425  < 2e-16 ***
ORIGIN_SZTSSZ06 -2.6310865  0.0255772  -102.868  < 2e-16 ***
ORIGIN_SZWCSZ01 -1.1561047  0.0087394  -132.286  < 2e-16 ***
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ORIGIN_SZWDSZ01  0.8712417  0.0043720   199.277  < 2e-16 ***
ORIGIN_SZWDSZ02  0.9119539  0.0050326   181.210  < 2e-16 ***
ORIGIN_SZWDSZ03  1.6205678  0.0045250   358.136  < 2e-16 ***
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ORIGIN_SZWDSZ05  0.4284783  0.0052752    81.224  < 2e-16 ***
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ORIGIN_SZWDSZ08 -0.8764983  0.0082622  -106.085  < 2e-16 ***
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ORIGIN_SZYSSZ03  2.0577240  0.0046737   440.274  < 2e-16 ***
ORIGIN_SZYSSZ04  0.8697472  0.0047269   184.000  < 2e-16 ***
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ORIGIN_SZYSSZ09  1.2274518  0.0044951   273.066  < 2e-16 ***
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DESTIN_SZAMSZ05 -1.0794168  0.0062543  -172.588  < 2e-16 ***
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DESTIN_SZAMSZ08 -0.9756903  0.0068829  -141.756  < 2e-16 ***
DESTIN_SZAMSZ09 -1.0362692  0.0061651  -168.087  < 2e-16 ***
DESTIN_SZAMSZ10 -0.1227646  0.0044788   -27.410  < 2e-16 ***
DESTIN_SZAMSZ11 -0.4802374  0.0088108   -54.506  < 2e-16 ***
DESTIN_SZAMSZ12  0.2142621  0.0050653    42.300  < 2e-16 ***
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DESTIN_SZBDSZ03 -0.1568727  0.0044329   -35.388  < 2e-16 ***
DESTIN_SZBDSZ04  0.6731669  0.0036215   185.882  < 2e-16 ***
DESTIN_SZBDSZ05  0.3647198  0.0040496    90.062  < 2e-16 ***
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DESTIN_SZBKSZ01 -1.2688264  0.0067263  -188.637  < 2e-16 ***
DESTIN_SZBKSZ02 -0.3912129  0.0055446   -70.558  < 2e-16 ***
DESTIN_SZBKSZ03 -0.8663392  0.0058693  -147.605  < 2e-16 ***
DESTIN_SZBKSZ04 -0.1247273  0.0051254   -24.335  < 2e-16 ***
DESTIN_SZBKSZ05 -0.7407774  0.0059120  -125.300  < 2e-16 ***
DESTIN_SZBKSZ06 -0.9934643  0.0063345  -156.834  < 2e-16 ***
DESTIN_SZBKSZ07  0.0882230  0.0042928    20.551  < 2e-16 ***
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DESTIN_SZWCSZ03 -2.7360882  0.0325753   -83.993  < 2e-16 ***
DESTIN_SZWDSZ01  0.8193492  0.0037301   219.657  < 2e-16 ***
DESTIN_SZWDSZ02 -0.7852474  0.0058655  -133.875  < 2e-16 ***
DESTIN_SZWDSZ03  0.5742422  0.0041884   137.104  < 2e-16 ***
DESTIN_SZWDSZ04 -0.8391525  0.0065075  -128.951  < 2e-16 ***
DESTIN_SZWDSZ05 -0.3510692  0.0057253   -61.319  < 2e-16 ***
DESTIN_SZWDSZ06  0.1358804  0.0043968    30.905  < 2e-16 ***
DESTIN_SZWDSZ07 -0.2207379  0.0066369   -33.259  < 2e-16 ***
DESTIN_SZWDSZ08 -0.0264655  0.0065065    -4.068 4.75e-05 ***
DESTIN_SZWDSZ09 -0.2065828  0.0050524   -40.888  < 2e-16 ***
DESTIN_SZYSSZ01  0.7467996  0.0040979   182.238  < 2e-16 ***
DESTIN_SZYSSZ02 -0.3002718  0.0053434   -56.195  < 2e-16 ***
DESTIN_SZYSSZ03 -1.1087686  0.0057219  -193.778  < 2e-16 ***
DESTIN_SZYSSZ04 -0.3748076  0.0051481   -72.805  < 2e-16 ***
DESTIN_SZYSSZ05 -1.7909654  0.0102064  -175.475  < 2e-16 ***
DESTIN_SZYSSZ06 -1.8519179  0.0099601  -185.933  < 2e-16 ***
DESTIN_SZYSSZ07 -0.9246626  0.0118101   -78.294  < 2e-16 ***
DESTIN_SZYSSZ08  0.4403129  0.0041268   106.697  < 2e-16 ***
DESTIN_SZYSSZ09  0.0267012  0.0041393     6.451 1.11e-10 ***
log(dist)       -0.6721961  0.0001353 -4969.566  < 2e-16 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

(Dispersion parameter for poisson family taken to be 1)

    Null deviance: 60796037  on 14733  degrees of freedom
Residual deviance: 20988409  on 14175  degrees of freedom
AIC: 21081154

Number of Fisher Scoring iterations: 7
CalcRSquared(dbcSIM$data$TRIPS, dbcSIM$fitted.values)
[1] 0.5739638

Model comparison

model_list <- list(unconstrained=uncSIM,
                   originConstrained=orcSIM,
                   destinationConstrained=decSIM,
                   doublyConstrained=dbcSIM)
compare_performance(model_list,
                    metrics = "RMSE")
# Comparison of Model Performance Indices

Name                   | Model |     RMSE
-----------------------------------------
unconstrained          |   glm | 4288.012
originConstrained      |   glm | 3659.954
destinationConstrained |   glm | 3389.556
doublyConstrained      |   glm | 3252.297

The print above reveals that doubly constrained SIM is the best model among all the four SIMs because it has the smallest RMSE value of 1487.111.

Visualising fitted values

Firstly we will extract the fitted values from each model by using the code chunk below.

df <- as.data.frame(uncSIM$fitted.values) %>%
  round(digits = 0)

Next, we will join the values to SIM_data data frame.

SIM_data <- SIM_data %>%
  cbind(df) %>%
  rename(uncTRIPS = "uncSIM$fitted.values")

Repeat the same step by for Origin Constrained SIM (i.e. orcSIM)

df <- as.data.frame(orcSIM$fitted.values) %>%
  round(digits = 0)
SIM_data <- SIM_data %>%
  cbind(df) %>%
  rename(orcTRIPS = "orcSIM$fitted.values")
df <- as.data.frame(decSIM$fitted.values) %>%
  round(digits = 0)
SIM_data <- SIM_data %>%
  cbind(df) %>%
  rename(decTRIPS = "decSIM$fitted.values")
df <- as.data.frame(dbcSIM$fitted.values) %>%
  round(digits = 0)
SIM_data <- SIM_data %>%
  cbind(df) %>%
  rename(dbcTRIPS = "dbcSIM$fitted.values")
unc_p <- ggplot(data = SIM_data,
                aes(x = uncTRIPS,
                    y = TRIPS)) +
  geom_point() +
  geom_smooth(method = lm)

orc_p <- ggplot(data = SIM_data,
                aes(x = orcTRIPS,
                    y = TRIPS)) +
  geom_point() +
  geom_smooth(method = lm)

dec_p <- ggplot(data = SIM_data,
                aes(x = decTRIPS,
                    y = TRIPS)) +
  geom_point() +
  geom_smooth(method = lm)

dbc_p <- ggplot(data = SIM_data,
                aes(x = dbcTRIPS,
                    y = TRIPS)) +
  geom_point() +
  geom_smooth(method = lm)
ggarrange(unc_p, orc_p, dec_p, dbc_p,
          ncol = 2,
          nrow = 2)